If you are to be given help with this, would you consider trying to repair this PSU?
Reason I ask/suggest this is because:
1) It's unlikely you will find a modern replacement in this form factor and with decent ratings on the 5V rail, which is what your P3 rig needs (though at least it's a P3 and not a slot A or later AMD, which tend to be much heavier on the 5V rail, making it even harder to find a replacement PSU with a good 5V rail in this form factor.)
And if you go with a NOS PSU, chances are, it will need a recap (i.e. work) to be safe/stable to use.

2) Astec PSUs were some of the best OEM PSU you could get back in the day. Almost always, they use high quality Japanese electrolytic caps and are very over-built. That said, some Japanese cap brands did have issues with a few particular series - namely, United Chemicon LXF, Nichicon PR and to lesser extent PL series. So if any of these are in your PSU, all you might have to do is just give it a recap.

But I'll let the others chime in here if someone has better options to suggest.
Worst case, consider finding another Astec PSU with the same exact model number. It's possible that this one might have suffered from a surge or other external factor rather than failed from wear/ageing. FWIW, all of my Pentium II/3/4 PCs with Astec PSUs are still going strong. They just needed the occasional dusting to keep them in good shape.