1984 suburban is not geting power from the key to the starter

You just don't have a power connection. Clean the cable ends at the battery and the starter and be sure they are tightened properly. Even a touch of power in the battery will at least turn the dash lights on. Just be sure your connections are clean.

try finding a broken wire , usually at the starter solenoid trigger terminal

Check fuses, check battery is charged.

You may need a shop to look at it, or get a used shop manual from Ebay to get the necessary wiring diagrams. The problems could be related, such as the key switch or the main wiring harness.
You say the dome light fuse is draining the battery, is one of the interior lights staying on ?

check that you have the starter wire on the solenoid correctly
whne you say power to the starter --is that from the battery lead or the small control wires from the ignition switch

Electrical power is getting 2 the sttarter solenoid but not 2 the starter. Make sure all wire 2 the starter r good & nuts r tight on starter & on battery. Battery should read approx 14 volts, 11volts or less bad battery. Make sure ground wire from battery is good & connected properly. Remove any wires suspect clean all connections retry.

Sounds like a brush sticking in the starter motor.

http://www.autozone.com/shopping/repairGuide.htm?pageId=0900c1528003dd2f#hd1-1-1

an easier way to do this and a more reliable method is to just using the directions above, completely remove the locking system and put in a painless switch. Its used on a lot of older hot rods. and only controls the starter not the steering colum lock. Its your call on that one, but I would use this method because it wont break again.

Check the wires on starter solenoid to make sure they are in the right spot. Sounds like the ignition wire terminal on the solenoid is getting constant power. I hope this helps!

He has evidently hooked up the battery directly to the starter motor. Double check which post the battery is connected to on the starter. ALWAYS disconnect the negative(-) on the battery when doing this kind of work. I have seen really bad things happen. MM85