Also check the voltage on your power supply with a voltmeter to make sure it's outputting close to 5 volts. Some Atari supplies are known for failing in a way that will damage components on the motherboard by over-volting them - RAM in particular.
Thanks, I assume the old PSU damaged the unit at this point. Any ideas of how to test them?
Is there a cheap place to get a whole motherboard?
Brown/red screen usually means that the OS isn't able to complete the earliest stages of powerup (after a soft delay of about 1/2 a second the IO registers are cleared which forces a black background, by default GTIA will often startup with a brown background and sometimes PM stripes overlayed).
That's a good sign which means the CPU, OS and MMU are probably OK. But it might mean that the Ram or Antic isn't OK. My guess would be that you have one or more bad Ram chips.
The quick/easiest way to diagnose is leave it on for several minutes, then put a finger on each chip in turn. Any that are hotter than the others are probably bad.
Quick/easy first thing to try is gently pry each one up then reseat but seeing it's an XE it's likely all the Ram is soldered in and most/all of the other chips the same.
Check the branding on the Ram chips. MT are notorious for going bad, if you have those then the best procedure is to replace all of them even if only a few are known to be bad.
How easy that job is can be dependant on which revision board you have. Early ones used 16 1-bit Ram chips so potentially a lot of work. Later ones use just 4 4-bit Ram chips which means a lot less work, and also the chips used are more easily obtained.
So I ordered a tested PSU and plugged it in and no change- still get the black screen.
So I tried the heat test- the only chips that were warm to the touch (ok maybe even hot) were the CPU, ANTIC, and GTIA after a few minutes. Is this normal? Is the memory supposed to be hot?
I have an extra personality board from an atari 800 that I could remove the chips from and "piggy back" them on to see if it's any of those if that's worth trying? Would they be compatible?