Do you have removeable side panels on your tower? If so, remove them and there will be set screws that go through the tower chassis into the sides of the power supply.
Warning: I’ve never seen a Dell Optiplex GX260, I don’t work for Dell, I work for one of their competitors.
Desktops are typically built with a chassis and two side panels. If your power supply seems to be held in place by invisible screws it could be that the working end of these screws is hidden under one of the side panels. See if you need to remove the side panel to get at them.
Dell OptiPlex GX260 Power Supply Replacement
https://www.ifixit.com/Guide/Dell+OptiPlex+GX260+Power+Supply+Replacement/4005
while you’re inside, be sure to vacuum up dust and check the CPU fan too.
BTW, there are two covers on your PC.
Take em both off. Not easy to figure out the second cover but, it does come off.
I’ve replaced the P/S plenty and been frustrated by this.
Obviously the best way to replace a politically correct power supply is with a non-politically correct one, such as coal or nuclear. ;-)
https://www.ifixit.com/Guide/Dell+OptiPlex+GX260+Power+Supply+Replacement/4005
This is a pretty good guide, better than I could explain
What ever you do, never ever purchase an Antec power supply or ANY Antec products.
Antec support people and customer service are the worst of the worst.
Dell Optiplex GX260 can have the issue with bad capacitors. Dell had a class action lawsuit against them because they knew they sold millions of pc’s with the bad parts.
https://www.ifixit.com/Wiki/Dell_OptiPlex_GX260_Troubleshooting
http://news.cnet.com/PCs-plagued-by-bad-capacitors/2100-1041_3-5942647.html%22
I’ve replaced several power supplies on my desktop and it is pretty much an easy job once you get the screws out. While you have the case open be sure to remove the dust from the heat sinks, motherboard and fans. Carefully use on of those canned air products. I have done two complete rebuilds of my custom built desktop. While laptops and tablets are great you can’t rebuild or even easily add RAM to them
Thanks to all. I discovered the P/S is held in place by slide-on socket tabs underneath the unit. The P/S has to be slid with some force forward, at which point the sockets disengage. No hardware is involved.