Here is a picture of the internals of the Astec (I think it's an XT PSU):

https://imgur.com/ZQ5b3lZ

I don't see any blown caps.

This looks like a full size AT PSU to me.
I doubt you're going to find a new one anymore but there's usually enough space in there to hack the innards of an ATX PSU into one.

I also think I mostly misread the thread.
You can measure the fan's voltage with a multimeter (I assume it's 12V) and simply swap a fan of the same voltage and physical dimensions into it. You can reuse the old fan connector cable by either cutting it and soldering the wires to the corresponding wires on your new fan or unsoldering the old cable from the old fan and resoldering it to the corresponding pads on your new fan. It's pretty self explanatory.

Thanks for the tips. Which PSU are you saying is full size AT? The Power Tronic is probably full AT but the Astec looks similar to this XT to me: https://www.ebay.com/itm/IBM-PC-XT-PS-Power-S … ic/284013203471

Yeah, sorry I didn't pay attention reading at first and subsequently messes up that post.
The Power Tronic looks standard full size AT to me. I mentioned that in regards to the "structure that requires the power connector to be located beneath the fan".

Both PSUs can probably be hacked to accept the innards of a new ATX PSU.

Got it. That sounds like a project. Is there a good thread on troubleshooting a "dead" PSU? If it's not a complex task, I'd like to repair the Astec.

I don't think there's such a thread - plus usually I'm all pro diy repairs but in this case I would advise against it:
-If one part in a power supply failed there's an increased probability of other parts having degraded or being close to failing. Worst scenario on a PSU is the loss of all hardware connected. If you need a guide on how to troubleshoot a PSU you are likely not able to thoroughly check the components.
-Also if you need a guide on troubleshooting a relatively simple PSU I can only assume you're an electronics beginner. It is probably best to start practicing with circuits that do not connect directly to mains voltage.
I would suggest to instead look for a retired technician or somebody similar who will guide you through the process for a sixpack of beer. Maybe there's a hackspace or a repair cafe near you with people that'll also be able to help you and teach you.
This is just my two cents, I don't mean to be a dick and I can only make assumptions based on what little I have read from you. If I'm wrong in my assessment or you simply want to do it yourself anyway I won't tell you you're not within your right to do so. 😉