Small form factor Dell GX620 systems were plagued by bad capacitors. Some in the power supply, others on the system motherboard. I don’t recommend replacing components in the power supply, but the capacitors on the motherboard aren’t too hard to replace.
If your Optiplex 620 power light goes amber, or the system starts shutting down due to “thermal events”, open the case and check the five capacitors I have highlighted below.
If the top of any of them is bulging at all, (or leaking like the one in the back of my picture) you should replace all of the ones I’ve highlighted. You can order them from an online source $6.
I am not a pro at (de)soldering by any means, but I was able to remove the board, replace the capacitors, and re-assemble the system in about an hour. I’ve replaced them on two systems so far and both systems are running like new.
Here are links to the parts I used. (UPDATED: 2/2017)
1800uF 8mm 6.3v (x1)
2200uF 10mm (I’ve talked to the website owner and these are out of stock)
2200uF 10mm 10v – these should be used instead (x4)
Good luck, let me know if you’ve tried this and how it turned out.