Dash lights don't work

Did you look at a wiring diagram to see what all is involved in those circuit's ? The fuse is GOOD ? 10 amp tail lamp fuse is good , but is there Battery + voltage there ? With a volt meter or test light check for B+ voltage on both sides of the fuse . Both the dash and tail lights get B+ voltage from the head lamp switch . You can find a wiring diagram here http://www.bbbind.com/free_tsb.html How to Use Multimeter to Troubleshoot Common Problems

Is there battery voltage at the coils ? Test with volt meter Two wires at coils 1 battery voltage the other ECM control . does you vehicle have a tachometer , if so does it move when cranking over the engine ? If not possible crank sensor. Any lights lit on dash , SECURITY ?

The regulator is inside the alternator. Get a new alternator or disassemble the alternator and install a new one. My option is get another alternator.

Did you look at wiring diagrams to see if all of these have anything in common ? Ground connection , B+ power supply etc..... Then testing the circuit's with a DVOM - digital volt ohm meter . Voltage drop testing .
Mastering Voltage Drop Testing with Pete Meier and Jerry Truglia
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Did you replace the indicator flasher relay in AUX relay box 2 ?
Free wiring diagrams here http://www.bbbind.com/free-tsb Enter vehicle info. year , make , model an engine size. Under system click on lighting ,then under subsystem click on turn signal lamps . Click the search button then the blue link.
Track it down , where do you have B+ an don't .

So your dropping battery or alternator voltage before
it gets to the lights

Why is your mission

A dirty or loose ground, thus incomplete circuit

Something in the circuit before the head lights?

You need to unplug one lamp & put your volt meter to
the 12v feed to that lamp & turn them on

If you "don't "drop battery voltage there at the end of the line ,
then you need a wiring diagram to work your way back to
the offender.

So,lack of ground or resistance in the form of bleeding off
volts before the lamps, that should get full battery supply

It could be the low oil pressure warning light. That light looks like an oil can with one drip of oil on the tip.
If that is the light it is telling you the oil pressure in the engine is low.
You might want to check with a dealer to make sure if you don't have an owners manual.

Thanks for choosing FixYa and welcome. Have you checked your tail lamp fuse and cluster fuse yet? If not, check them. You could have an electrical issue. You may have a bad wire or loose wire somewhere. In order to find out, you will need to test the wires in the harness with a voltage meter to find which wires don't have current.

I can't speak for the engine light issue, but look into stepper motors for your gauges for the oil pressure issue. I just purchased a used '04 Trailblazer EXT and the tachometer stopped working 1 week after driving it off the lot. I did some looking and apparently the Delphi motors that GM used do not hold up. "Check this link for more info...
http://forums.trailvoy.com/showthread.php?t=48886

1. do the park lamps work?
2. dash lamp fuse burnt?
3. is the instrument cluster analog or digital?
4. digital clusters have been known to fail however the cluster lighting is controlled by a body computer.
5. proper diagnosis with require a scan tool that will access the body module ( computer)

check the vehicle speed sensor located on the transmission housing.