Good Idea freezing it could shift a bad solder point or other type of connection.
If it worked for a few moments then at least you would have some sort of confirmation of heat caused resitance somewhere.
I would visually look at it and if I don't see anything I would yank the drive as you said because its probably still good and put it in an enclosure or dock as some call it.
Sell the computer as broken w/o hard drive on Ebay (People like me buy them)buy another comp (Not an HP)from NewEgg. Retrieve data from old hard drive.
Probably not worth taking to shop.
Just pull the drive. Go to Best Buy and get something else.
I went in two months to pick another Sony VAIO for $1,800. They didn’t have the one I wanted so asked if they had anything comparable in terms of features.
They should me the Dell Studio 17 which happened to be on sale for $699.
Saved $1000 and the only thing I don’t care for is the screen. Sony has a better screen but, whatever, it does everything the other one was going to do.