What could be causing these problems and how to fix it?
 

I own a 1990 Cadillac Coup Deville with 89000 miles on it. Every time I turn on my car, the radio and clock restart itself, so the clock is at 1:00 and the station is 1400 am. The button to open my gas door is also not working, so I cannot open my gas door to get gas. I need help ASAP!!!! I need to get gas hahaha!

What could be causing these problems and how do I fix them?

Check your owners manual,there should be a "pull cord" on the left hand wall of your trunk to manually open the gas tank lid, there's one on my 92 eldo.

You have two separate issues most likely unless the gas lid release and radio memory are on the same circuit (power with key off)

I would start by having your battery load tested.

always check body and engine ground cables. There are several.

If battery voltage drops below 10 volts while cranking you will lose memory power for the radio.
If you lose radio memory when you hit the gas lid button then your getting close.

Fords did this also during the 80s into the 90s.

You have a fuse for accessories that is hot all the time- check your fuses- you have one out.

I like your answer better.

The cigar lighter fuse should also feed memory for radio. I think I misunderstood and thought he lost memory
While cranking.