If you have a bill of sale, with his signature on it, remind him of that fact, if he does nothing, drop him in the smelly stuff by going over his head. If you haven't, consider it one of life's great experiences, cos you sure as hell won't do it again.
I'm not up to date on QRs/MML but certainly in the past, to borrow money from a subordinate, whether repaid or not- was a serious office.
Quick check of the legal situation and then if that situation still prevails, a hint of the serious consequences of the knowledge getting around or, a quiet word to his superior along the lines of; I don't want to get Cpl X into trouble, but,,,
To owe money would be classed as the same as borrowing
might do the trick
I take it you are still in training? If so, your Corporal has broken the ATRA (or whatever it's called now) code of conduct. BUT....wait until you finish training and then pop into RHQ before you leave the unit and ask the Chief Clerk/RSM/CO (any grown you bump into up really) how you go about getting your money back from the Corporal who bought your TV off you.
Get a family member to phone the CO up (again....after you finish training) and ask how to get your money.......
You'll get your money and that pathetic tit will get what's coming to him as well.