Mac Mini A1103 (2005) Boots then immediately shuts off.

I have an old Mac Mini A1103 from 2005 and I have been trying to turn it on. It was working just fine 2 weeks ago but all of a sudden just 1 week ago when I opened it and cleaned it, the Mac just boots up and immediately after 20 seconds shuts down.

I have only used a brush and I was very careful and very sure that nothing got damaged. And even without the shell casing it still doesn't show any signs of damage!

The Power supply seems fine, but I don't want to buy a new one. I use this Mac Mini as a basic File server with OS X Tiger Server and I also have some old photos that I don't want to lose. Plus I just like the device in general.

Is there any way to save it?