To be honest I’m not very good with PlayStations, but USB ports actually have a very weird type of behavior when they’re broken. I don’t think that I’ve got any clear solution for this, but I’ve got some tips and tricks that you can try.
Broken USB ports can in fact still charge stuff up such as controllers, although transferring data might be impossible. If your USB stick worked with several computers the problem might just be the USB ports. Do some research and see if they have gotten damaged at any point. If that’s the case, a replacement of them might be necessary.
As I said previously I’m not very good with PlayStations, so the problem might also be the operating system. If it doesn’t support the files you are trying to transfer you will most likely get an error message or not find them at all. However if the PS3 doesn’t detect the USB stick at all, try and hook something else up to it (example: another USB stick) and see if that works.
If that worked I don’t have a solution for your problem. However if that didn’t work you should replace the USB ports and see if that will work. Or you could try resetting your whole system and see if that fixes the problem before buying anything, but doing so will wipe your data! So backup anything you want to keep.
I’m telling you again that I’m not very good with Playstations, but I hope that you will find a solution.