Whenever the 4WD diagnostic light stays on, the 4WD indicator lights will not come on. That's normal.
If the battery was low/dead for a long time, the self-diagnosis memory in the Transfer Control Unit may have been erased. If this is the case, driving around for a while should give it enough data and the 4WD light should go out.
If you have an ODBII code reader, you can check if there are any codes stored in the ECU. There is also a diagnostics mode you can go into for transfer case issues:
1. Warm up the engine. Turn it off.
2. Turn the ignition switch on and off at least twice, then turn the ignition switch to off.
3. Shift into park.
4. Turn the 4WD selector to Auto.
5. Turn the ignition switch to on. Do not start engine.
6. Is the 4WD warning lamp on? Continue if no.
7. Shift into reverse.
8. Turn the 4WD selector to 2WD, Auto, 2WD.
9. Shift into drive.
10. Turn the 4WD selector to 4H, Auto, 4H.
11. Shift into neutral.
12. Turn the 4WD selector to Auto.
13. Shift into park.
14. The 4WD indicator light will come on for 2.5 seconds, then go out. It will then flash a series of times to represent a one or two digit code, with half-second delays within a number and 1 second delay between numbers. e.g. to represent the code 23, it will flash twice with 0.5 seconds between flashes, wait a second, then flash three times with 0.5 seconds between them. If there's a number, reply and I'll look up the code for you.
If the light just flickers with 0.25 second delays, the memory is the problem and just driving around should fix it.
If there's no light on, either you did it wrong or the one of the PNP (park/neutral position) or 4WD switch circuit is open.