Without pointing fingers at Jensen TV, most manufacturers (Keystone included) buy components in bulk from the lowest bidder, so usually the TV's included are not the "best quality" and sometimes aren't even available at local stores. It doesn't suprise me that you had an issue with the TV and would make an "educated guess" that you suffered a "major meltdown" somewhere in the RF receiver. If the TV still turns on, still has a "menu" function yet there's no picture or sound, it would probably be cheaper to get a new one than to try to repair the broken one.
If you're still in the 1 year Keystone warranty, call your dealer, if not:
It looks like you've tried to verify that it is the TV by connecting it to a "known good antenna output." I'd take it into the house, try it there on a good RF cable input and, if it still won't work, it's up to you whether to spend money to get it checked out or simply replace it. Keep in mind that most electronics service shops will charge you a diagnostic fee of $50 or so to check it out (and apply that to the repair if you say yes). So, even if you have it checked out and decide it's too costly to repair you will still owe the fee.
19" through 22" LCD sets are going for less than $100 on sale many places, 26" for about $139 and 32" for less than $200.
Yes, we seem to now live in a disposable society