Can a1999 4x4S10 Blazer be Dinghy towed without a Neutral light at the 4x4 switch

What do you mean by "dinghy"?

Some customers may want to tow their vehicle behind another vehicle with all FOUR tires on the ground. This is referred to as "dinghy" towing.
Towing in this manner is acceptable only on the certain vehicles. The vehicle should be properly equipped and prepared as described below.
The passenger cars listed above are the vehicles that CAN be dinghy towed. Passenger cars not listed above are vehicles where dinghy towing is not permitted or recommended.
Certain 4WD trucks can be dinghy towed depending on the transfer case option. Rear wheel drive and AWD trucks should NOT be dinghy towed. Refer to the truck models and transfer case options below.
Please refer to the applicable vehicle Owner's Manual before towing.
Passenger Cars Notice: These vehicles must not be towed backwards or transmission damage may occur.

• 1995-2005 Chevrolet Cavalier, Pontiac Sunfire and 1996-2000 Toyota Cavalier equipped with Hydra-Matic® 4T40-E Automatic Transmission (AT) (RPO MN4) or 5-Speed Manual Transmission (MT) (RPOs MK7, MJ1, M86, M94) • 1995-2005 Pontiac Grand Am equipped with Hydra-Matic® 4T40-E or 4T45-E AT (RPOs MN4, MN5) or 5-Speed MT (RPO MJ1, M86, M94) • 1995-1998 Oldsmobile Achieva equipped with a 5-Speed MT (RPO MJ1) • 1997-2003 Chevrolet Malibu, 2004-2005 Chevrolet Classic and 1997-1999 Oldsmobile Cutlass equipped with Hydra-Matic® 4T40-E AT (RPO MN4) • 1999-2004 Oldsmobile Alero equipped with Hydra-Matic® 4T40-E or 4T45-E AT (RPOs MN4, MN5) or 5-Speed MT (RPOs MJ1, M86, M94) • 1994-1997 Geo Tracker / 1998-2004 Chevrolet Tracker 4WD models equipped with 3L30 or 03-72LE AT (RPOs M41, M65, MX1) or 5-Speed MT (RPO M59) • 2006-2007 Chevrolet HHR • 2005-2007 Chevrolet Cobalt, Pontiac Pursuit • 2005-2007 Pontiac G6 (excluding 3.9L V6 AT) • 2007 Pontiac G5 • 1995-2005 Chevrolet Cavalier, Pontiac Sunfire and 1996-2000 Toyota Cavalier equipped with Hydra-Matic® 4T40-E Automatic Transmission (AT) (RPO MN4) or 5-Speed Manual Transmission (MT) (RPOs MK7, MJ1, M86, M94) • 1995-2005 Pontiac Grand Am equipped with Hydra-Matic® 4T40-E or 4T45-E AT (RPOs MN4, MN5) or 5-Speed MT (RPO MJ1, M86, M94) • 1995-1998 Oldsmobile Achieva equipped with a 5-Speed MT (RPO MJ1) • 1997-2003 Chevrolet Malibu, 2004-2005 Chevrolet Classic and 1997-1999 Oldsmobile Cutlass equipped with Hydra-Matic® 4T40-E AT (RPO MN4) • 1999-2004 Oldsmobile Alero equipped with Hydra-Matic® 4T40-E or 4T45-E AT (RPOs MN4, MN5) or 5-Speed MT (RPOs MJ1, M86, M94) • 1994-1997 Geo Tracker / 1998-2004 Chevrolet Tracker 4WD models equipped with 3L30 or 03-72LE AT (RPOs M41, M65, MX1) or 5-Speed MT (RPO M59) • 2006-2007 Chevrolet HHR • 2005-2007 Chevrolet Cobalt, Pontiac Pursuit • 2005-2007 Pontiac G6 (excluding 3.9L V6 AT) Towing Procedure Notice: Failure to follow these instructions may result in damage to the transmission.
Important: The towing speed as stated in the Owner's Manual should not exceed 104 km/h (65 mph) for 1995-2005 vehicles.
In order to properly dinghy tow the vehicle, follow these steps:

1. Firmly set the parking brake.
2. Open the fuse panel and pull the fuse(s) indicated in the Owner's Manual section detailing towing your vehicle. This prevents the instrument panel (IP) and/or electronic PRNDL indicator from draining the battery.
3. Securely attach the vehicle to the tow vehicle.
4. Turn the ignition key to the OFF position, which is one position forward of LOCK. Unlocking the steering column allows for proper movement of the front wheels and tires during towing.
For 1997-1999 Cutlass, 1997-2003 Malibu, 2004-2006 Chevrolet Classic and 1999-2004 Alero/Grand Am models, turn the ignition switch to the accessory (ACC) position, which is one position forward of OFF. This position unlocks the transaxle.

5. Shift the transmission to Neutral (N).
Notice: Use extra care whenever towing another vehicle. Do not exceed the towing vehicle's gross combination weight (GCW) by adding the weight of the dinghy towed vehicle or vehicle damage may result.

6. When the vehicle being towed is firmly attached to the tow vehicle, release the parking brake.
7. Replace the fuse(s) in the fuse panel when finished towing.

best solution is to remove the driveshaft to the rear, and disengage the front hubs

The neutral tow kit is nothing more than a LED to indicate that the transfer case is in neutral. I installed my own LED and had the dealership download the program. This is for 2001 - 2005. The tow indicator light plugs into the small green connector under the steering wheel. I cut the connector off and installed straight line wire connectors and hooked it up to the LED. I had the dealer confirm that following the sequence of steps the transfer case was in neutral. Make sure the vehicle is secured (won't roll away)
1. have the engine running
2. put the shift level into neutral
3. turn the key back one position (off but not locked)
4. indicator light wil come on and then turn off
5. press the brake and the 4X4 auto button for about 5 seconds
6. the indicator light will flash 4 times and then stay on
7. release the brake and the 4X4 button
8. transfer case is in neutral

you should be able to tow it with the transfer case in the nuetral position.

Yes it can, just place your Transfer Case in Neutral position.
Shifting into NEUTRAL
To shift the transfer case to NEUTRAL do the following:

Make sure the vehicle is parked so that it will not roll.
Set the parking brake.
Start the vehicle or turn the ignition to RUN.
Connect the vehicle to the towing vehicle.
Put the transmission in NEUTRAL (N).
Shift the transfer case to 2HI.
Simultaneously press and hold the 2HI and 4LO buttons for 10 seconds. The red NEUTRAL light will come on when the transfer case shift to NEUTRAL is complete.
Shift the transmission to REVERSE (R) for one second, then shift the transmission to DRIVE (D) for one second, or FIRST (1) for vehicles equipped with a manual transmission.
Turn the ignition to LOCK.
Place the transmission shift lever in PARK (P), or FIRST (1) for vehicles with a manual transmission.
Release the parking brake prior to towing.
Shifting Out of NEUTRAL
To shift out of NEUTRAL:

Set the parking brake and apply the regular brake pedal.
Shift the transmission to NEUTRAL (N) and turn the ignition to RUN with the engine off.
Press the button for the desired transfer case shift position (2HI, 4HI, AUTO 4WD or 4LO).
After the transfer case has shifted out of NEUTRAL the red light will go out.
Release the parking brake.
You may start the engine and shift the transmission to the desired position.
Excessively shifting the transfer case into or out of the different modes may cause the transfer case to enter the shift protection mode. This will protect the transfer case from possible damage and will only allow the transfer case to respond to one shift per 10 seconds. The transfer case may stay in this mode for up to three minutes.
NEUTRAL: Shift the vehicle's transfer case to NEUTRAL only when towing your vehicle.
Good luck and hope this answers your question.

It seems to be stuck in 4x4 still. There could be damaged done to the powertrain by the towing company. Therefore they should be held accountable for the damage and repair that will be needed. You never tow a vehicle in 4x4 it should be carried on a flat-back. Same with AWD vehicles. The towing companies are well aware of this, is their business to know. Make sure to disengage the 4x4, put the 4x4 shifter on the floor in neutral while in park or not moving. If you continue to have problems contact the towing company and hold them accountable for it. See what you can work out with them. If they tell you they are not responsible then contact a lawyer and make them responsible for it.

I would think if transfer and trans. are in neutral it would not matter how fast you go with in reason.

maybe changing the actuator is the next step. it may pull but not hard enough to engage the front axle

If you are sure the transfer case is in neutral, yes. There will be no damage to transmission.