Does sound like a condenser mic, which does need a HT power supply to put charge on the plates. Might be the caps...or might not be. Lot of twaddle talked on the interweb. There was a great panic maybe 15 years ago, when a cap company produced great batches of duff electrolytics. They went into everything - TVs, computer power supplies etc - and caused absolute chaos. Worth swapping them out as a first step. You’d likely have to look at folk like Farnell to source the correct surface mount capacitors. Failing that, can you get a new power supply?
Could be lots of things, but you could try poking around with something non metallic to see if anything has come desoldered and is loosing contact as it shifts on warming.
My trusty soldering iron is a Weller PS-D3 liberated from an old employer. Well actually it was my year in industry. We asked if we could keep our tools at the end of the year, but were told that the soldering irons had to be returned - which I duly did, but only after nicking one off a full time employee. Sorry John Wilcox (He engraved his name on it!) End of confession
I believe you can get a USB lead with double connectors at the computer end so I'll probably try one of those first. Likely I'll end up buying a mic that doesn't need phantom power. I had a nice AKG once that I pinched from the UK Subs as they passed by. Punk innit.
Static like noises will probably be a cracked solder joint or a crack on a component that warms up - not the big capacitors, but some surface mounted ceramic capacitors.