If this is the "small form PC" then do the following:
If the PSU has any LEDs on itself, check the status(not frt. panel) and using the manual what they refer to, LED sequence. If not present, then with AC removed, open case and reset all power cables and main PSU cable itself at mtrbd.. Assure all is OK and then return AC cord and try to power-ON. If it works, great. If not, does it do the same? Then with cover still off, inspect the mtrbd. for "bad caps", google for examples use bad caps as keywords. It needn't be a real bad cap, minor damage is very common and prevents the PC from booting up. If not the problem, then you're left thinking the PSU is bad, then reduce the load to the PC, disconnect all drives and see if that gets further. Bad caps it just too common on small form PCs and if this is dated PC, it's showing it age due to wear&tear.
Since, you know now how to access the innards of the PC, please note if you buy another PSU be sure its the same type. Dell provides on the PSU itself some decal/sticker and thus model#, use that to find replacement. Basically, you want a physical match to it fits and hopefully it larger wattage unit as well. if cost is a considerable, then that's up to you to decide.
if you plan to toss the PC, then remove HD and mount in an ext. USB case or inside another PC as 2nd HD so you can retrieve any data. Of course, you jerry-rig the PSU with one found elsewhere and reconnect outside of case to get things done(just a thought).