2004 silverado 4 wheel drive does not work, 4 wheel high button remains lit, will not change to any other button

I guess you probably don't know what transfer case you have ?
SERVICE 4WD
Refer to
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Transfer Case Description and Operation in Transfer Case - NVG 149-NP3

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Transfer Case Description and Operation in Transfer Case - NVG 246-NP8

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Transfer Case Description and Operation in Transfer Case - NVG 261-NP2

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Transfer Case Description and Operation in Transfer Case - NVG 263-NP1

The NVG 246 EAU provides 5 modes, Auto 4WD, 4HI, 4LO, 2HI and Neutral.
The four manual mode, or range gear positions, of the NVG 261 transfer case are:
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2HI - 2 wheel drive high range

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4HI - 4 wheel drive high range, part-time

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4LO - 4 wheel drive low range, 2.72:1 gear ratio reduction

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N - Neutral, 4 wheel

The NVG 263 transfer case provides the driver with 4 manual mode/gear positions:
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2HI - 2 Wheel Drive high range

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4HI - 4 Wheel Drive high range

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4LO - 4 Wheel Drive low range

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Neutral

With the info I've given you ,you should be able too now !
There is probably a code stored somewhere !
DTC B0790 DTC B2725 DTC C0300 DTC C0305 DTC C0306 DTC C0321 DTC C0327 DTC C0359 DTC C0374 DTC C0379 DTC C0550.

2 speed electric shift transfer case problems #1 jack up truck place on 4 jack stands. Start and select 4 high position in drive release brake ad watch front driveshaft does it turn "yes" problem is axle actuator on passenger side of differential not engaging axle shaft. "no" apply brakes bring to a stop engage low range does low range work "yes" internal transfer case problems "no" electric transfer case shifting motor failure.

If you have a lot of miles on it your 4wd trans.

The electrical wire came loose from the back of my 2H, had to take the panel off and re-soder it. Works fine now.

check all fuses if good then actautwaiter

try selecting from nutreul or less then 3km

the most likely cause is the front axle shift motor if bad your your front axle shaft will not lock in.if there is no shifting of transfer case there is also a electric motor that engages that in .

ARE YOU DOING IT WHILE IT'S IN NETRUAL, BEFORE YOU PUT IT IN GEAR AND WAITING FOR IT TO ENGAGE? IF NOT THAT IS YOUR PROBLEM.

It doesn't have manual hubs. Does this have a lever on the floor or push button 4 wheel

I ran across this problem with another vehicle....try putting it in another position (2 wheel high, 4 wheel high) and rocking it from drive to reverse, drive to reverse. Also try backing up at a pretty good clip and stepping on the brakes hard.....hope this works for you.