I own a 2002 Blazer with electronic 4X4. When i press either 4hi or 4low the lights blink on the push buttons and the four wheel drive never engages.

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.

Have you had codes checked ? While connected to a good scanner that will check transfer case switch to show if switch is working, and it could be the switch on the side of the transmission.

I have a 1999 blazer every thing is engaging and says it is in four high but the front wheels is not pulling

Ineed to know what kind of shifting system you have. Is it a shift lever or a push button systemThe fact that it works sometimes is a good sign. So this means its not completely broken and could be a simple adjustment

Hi, depending on the vehicle, there can be different controls. Standard control, 4hi, use in slippery conditions, never on dry pavement. Just push the button, and it will engage. 4low is for extreme conditons and the transmission must be in neuteral to engage 4lo. If you have auto 4wd button, just press the button in slippery conditions. If you have a denali, it is all wheel drive, and there are no buttons to push. So, depending on the model, there are multiple ways, but pushing the button engages it. Good luck...Goop

you need to be in neutral with the truck moving less than 3 mph for the truck to allow itself to shift into four lo

fords are famous for this. Its electronically controlled 4x4(push button) i would start cheap and replace that switch

try seeing if the cable going to the front differental is pulling in to engage the front axle?

I had this on my 2002 blazer (4wd 4dr 6cyl) about a year and a half ago. I found two things out. First, have to try shifting out of 4lo while in neutral with foot on the break. It seemed to work better while on a small incline (like waiting to put the boat into the water, not on the ramp but the somewhere shortly before ramp).
I finally decided to try to replace the neutral safety switch after much reading online. It worked and has worked perfectly since then. The shops I took it to told me to put in a whole new motor for about $600. I think I got the safety neutral switch for about 50ish. I have a pit in the garage so it was pretty easy to get under the truck to the transmission and remove the existing switch board. I then just attached the new one and plugged 'er in.
Hope it helps, good luck.

Reset the computer by disconnecting the battery. This should solve this. nutetral is for the four lo only to engage.

Mike