My 2000 blazer won,t select 4wd hi/low or auto

S10 you said clearly. NO BOX told at all, of 3 or more.
post that transfer case is there, ?
some are part ,time only for offroad only.
how to shift, steps (in dirt best)
keyoff, stop engine
key on shift to 4hi 4wd not 4 Low, 2speed version .
now start engine.
see if that works.?
got 3 switch NP1 box or NP233c box. (part time 4wd offroad only()
or 4 switch NP8 box, np236' is not full time !!! it too is part time.
not sure what box is there me, ever, only RPO and rear tag on box tells me what is there.
NP# is RPO code off your cars RPO list
Is the transfer box dry, the pumps love to wear a hole in the case and leaks dry, did it?
quote the 236 pages (wobble eats out case)

A problem associated with the NP236 transfer case is input and or output bearing wobble wearing out the case. The case material is magnesium which can build up heat in the unit causing failure of range fork and range hub, we recommend that these items be replaced during the rebuild cycle. The NP236 is also susceptible to problems caused by running the NP236 transfer case on hard surfaces like concrete or asphalt. Run 4WD only on loose dirt, snow, mud, sand or grass as the different wheel speeds in turns can put excessive torque loads on clutch, chain and sprockets.
join a real; GM forum , tell them your vin and this allows RPO to be pulled up and your transfer case, is now known, if still OEM stock.

The reason the light is flashing constantly is because the vehicle is sensing that four wheel drive(4WD) is not working. These 4WD systems use vacuum from the engine to engage/disengage to front axle. The vehicle probably has no vacuum going to the front axle, which would not allow the 4WD shift to complete, which would then leave the light on the dash flashing.
First thing to check is that the vacuum actuator on the firewall is working as it should.

You have a switch on the instrument panel ?
The NVG 263 transfer case features a three button shift control switch located on the instrument panel
The NVG 236/246 transfer case features a 4 button shift control switch located on the instrument panel.
Or
The New Venture Gear (NVG) 261, RPO NP2 transfer case is a two-speed, part-time with "mode shift-on-the-fly" capability. It has a chain driven front output shaft and an epicyclical low range planetary arrangement. The NVG 261 transfer case features a four position shift lever control located in the vehicle floor plan. As required, the operator can select 4HI position from 2HI "on-the-fly," as described in the owners manual. A dash 4WD lamp will continue flashing during shifting, until all criteria have been met and the new mode/range position has been reached. Once the new mode/range position is fully engaged and the front axle disconnect locks in, the dash light 4WD indicator lamp will remain ON constantly. Range shifting functions similarly, although it should be limited to speeds 8 km/h (5 mph) or less.

Check the vacuum switch under the hood in the center of the firewall...follow vac diag

Sounds like the encoder switch is bad ..it on the transfer case .it has a motor with wires going to it.when you press the button it sends a signal to that motor to switch into a certain gear..

If you can't get 4 high, then you can't get 4 low either. You can get the transfer case to go into 4 low, but unless the front axle is engaged, you will still be in 2 wheel drive. There is a vacuum switch that engages the right front wheel. The left wheel is engaged full time. On earlier models, this vacuum switch is located unerneath the battery tray. It is prone to become disconnected from the vacuum line. Check this and all other vacuum lines that are connected to the 4wd system. The way I test my 4wd Jimmy is to find a dirt or gravel road or parking lot and accelerate hard from a standing start in both 4hi and 4lo. If 4wd is not engaged your back wheels will spin.

Check the fuse to your 4wd at the fuse panel at the end of the dash drivers side. If the fuse is good, put the transmission in neutral and listen for the Transfer case encoder motor to work when you push the button on the dash for 4wd hi then to 2wd. If you do not hear it working, inspect the wire harness at the Encoder motor to make sure there not damaged in anyway due to corrosion or disconnected.
Here's some info on how the 4wd system operates on newer Blazers for all those searching for the cause of the flashing dash switch light and no engagement.

4WD System Operation on 98 up (2nd Generation) Blazers/Jimmies

The front drive shaft always turns on “shift on the fly” systems so the drive train is at the same speed in the front as the rear or the whole thing would break when engaging 4Hi or Autotrac when moving. InstaTrac (NV243 case or NP1) has 3 buttons. AutoTrac (NV246 case or NP8) has 4 buttons and clutch packs in the transfer case and is the only system for on pavement driving! Prior were the NV231 (87-93) lever and NP233 (94-97) electric motor. Your VIN # is the only sure way the dealer can get correct parts/listings!
1. Select mode on dash switch
2. Signal goes to the Transfer case control module (TCCM) or computer located in the cab on the passenger side behind the kick panel.
3. If you want 4 Lo the TCCM commands the encoder motor on the transfer case to switch a lower gear in (requires putting the shifter in Neutral and be stopped or only going 2-3mph). Note that if 4 Hi selected no action done in the transfer case. The transfer case is chain coupled and has the low and high gear. You can put all systems into Neutral by pushing the 2Hi and 4Lo button at the same time when the key is in the run position (or running but not off or acc).
4. The left front (drivers side) CV axle is always engaged to the front differential, but the right side is not coupled in 2wd. There is an actuator located under the battery tray that when commanded is vacuum actuated and pulls a cable from it to the right side CV axle coupler engaging that axle. A sensor is on that axle that tells the TCCM the axle position.
5. On 99up there is an additional vacuum switch on the firewall that switches the vacuum on and signals the TCCM also.
6. The dash light on the selector switch flashes while all this is occurring and will not switch out of 2wd unless all parts report correctly – same on the switch to any mode or back to 2wd.

So, there are a lot of possible failure areas with actuators/computer/motor/sensors/vac hoses and a special scanner is required to read the codes when the Service 4WD light comes on. But, a few things can easily be done before going to the dealer.
1. Check all vacuum hoses from the intake to the drivers side reservoir can, then to the extra switch (99up) and down to the under battery actuator. Small hose is 5/32 and larger is 7/32”.
2. See if the actuator pulls the front axle cable to engage it. If not and all hoses are good the diaphragm may be leaking on the actuator. If it engages but the light is still flashing remove the indicator switch on the front axle (only electrical plug in there) and manually push it in with the connector plugged in and see if the light stops, if so replace.
3. Listen to the encoder motor clunk when 4 Lo selected. If not working look at the wiring going to it for any cuts/breaks and repair if any found. Another indicator switch on top of this case. The fluid in the AutoTrac case should be the newer light blue Autotrak –II synthetic P/N 12378508 ($7 qt) not the red Dexron III.
4. If the light keeps flashing after this then disconnect the battery for 30 minutes for a TCCM reset, just make sure you turn off your radio first.
5. Still not working – take it to the dealer and stop at the bank on the way for $$$$!
12577412 is the part number for the Transfer Case Control Module (TCCM), or you can do the Salvage Yard for $15.00 if that's the part that has gone bad.

check the solenoid on the front differential. i had a similar problem. when i would start to engage 4wd low/high and it would blow the fuse. i replaced the front solenoid and fixed my problem.

the solenoid can be found in the right side of the front differential. costs about $100 at local part store and takes 5-10 to changeout with an adjustable wrench.

the transfer case module is bad it is bolted to transfer case above front drive shaft

yea its not shifting again like before ? sounds like your transfer case solonoid has possably gone bad again .. these are a sometimes dont work item .. It is what shifts the transfer case into gear and it might be a little worn or weathered and not letting the switch kick it in gear all the way from the N position. thanks Jerry holler if you need more.