Domestic TV sets radiate all sorts of noise through the antennas they are connected to. Placing a scanner receive antenna alongside/next to your TV antenna is a great way of loading up it's front-end with rf noise.
Scanner/receiver front-ends are broad-band - designing and incorporating a 1Gig plus front-end into something that costs what a Radio Shack scanner/receiver costs is going to lead to comprimises (big time comprimises) - even companies like IZT Labs, Roke Manor, Rhode & Schwarz, Watkins Johnson, Agilent ect ect ..... all "struggle" to design & build broadband receiver front-ends to budget (and the cost of their gear is many times more than the typical consumer scanner receiver).
First thing to do, before anything else is to establish if indeed the TV set is the problem: compare demodulated scanner/receiver reception with the TV set plugged in & switched on versus switched off and unplugged. If there is little to no difference then obviously your TV set is not to blame ........ that antenna farm with its 1300ft tower combo down the road becomes a good suspect.
In any event - it all comes back to much the same problem i.e. the ability of your Radio Shack scanner/receiver front-end to handle "noise". It's limited - very limited.
Do some reading up on preselectors/preselection and band filters (in band, band pass ect ect ..). You'll be shocked just what an impact (for the better) carefully chosen aftermarket preselectors and/or filtering has on the ability on any scanner/receiver to receive, process & demodulate rf.