OK, I use GX280s as home servers and ran into a similar problem with one of them...
The problem may be serious and not worth fixing (motherboard).
Turn power on
Fan(s) come on full power, sounds like a jet engine, or eventually gets that loud.
See if you power light has gone amber.
You get nothing on the screen, no Dell splash screen/post, nothing.
This is what I posted a while back concerning the above. Obviously I cannot bee 100% certain as I do not have your box in front of me. This a known issue.
-------- See if the power light goes amber after power up. I had
(have - still siting in my basement) one that did same. Power up, fans
go full blast . Power light goes and stays amber. This is USUALLY
caused by bad capacitors on the mother board. Known GX280 problem going
back. If you look on the motherboard, the capacitors should have flat
tops and not leaking. If the are rounded or leaking, the MB has
probably gone bad.
Bottom line this is usually a defective motherboard. Mine was a bad caps issue, you issue could be different, but it does sound like the motherboard.You can google "gx280 solid amber light loud fan" and see the issues. Here is one link.
I just replaced one of my old 280s with a dual core Dell Precision 390 workstation for about $118, and that included shipping, off of ebay.