Should I throw it away?

It has been stored in the attic for 12 months, I SWITCHED it on and it powered up, it was a bit noisy, then it switched off, now it won't switch back on. I wonder if the motherboard has shorted out or something, does it sound familiar to anyone? I'd be grateful for any adviceReplace the CMOS battery...part # CR 2032...available anywhere.....

And borrow a known good PSU and swap it in there to test...Noisy could be either a failed fan bearing, or fan that is grinding against something like wires inside that are mismanaged or a heatsink clogged with dust bunnies.

In one system a while back the customer told me that it was making a grinding noise like someone turned on an electric grinder inside of it and then it would shut down after like 10 seconds. When i opened it up I found that the 4 LOCKS for the socket 775 heatsink were snapped off the motherboard and the  CPU fan and heatsink were resting fan blade down in the case so when it was turned on the plastic blades were grinding the bottom metal and the heatsink was dancing hanging from its power connection on the motherboard.

Perform a visual inspection inside to make sure all looks good, NOTHING in the path or conflicting of fan blades and heatsinks attached properly vs resting face down on bottom of computer case.  The poster did not give the model # of the HP Pavilion desktop.
He might get a working version with new OS for about $120 on EBAY. Some of the refurbish companies offer one year warranty.

The idea is to have a source of spare parts to keep the refurbish unit going.
And provide a way to diagnose the old unit.

Could be a fun project.