So, there are three premium hotels in your market, all doing well. There are 3 economy motels there, (yours, his and the dead one). This tells me that the market is screaming for a mid level accommodation, and that's going to come from one of two places - either you are going to upgrade and fill it OR somebody is going to buy the dead motel and modify it to fill that void.
You are right there at that sweet spot. I recommend grabbing the opportunity at once! By all means get rid of the old TVs and put in flat screens. If the ones at the dead motel are really nice and new, get them if you can. Otherwise, just get nice new ones - they'll pay for themselves in energy savings and guest satisfaction. Even if your competitor gets the TVs, it just raises the tide for everybody.
Look at the rooms. It's not difficult to spruce them up. Make them look as clean and fresh as the premium hotels! Visit the premium hotels and steal a few ideas you can use to make YOUR place stand out from the other economy motel. If you run out of ideas, binge watch "Hotel Impossible".
Don't worry about your "competitor". You're about to hand him the entire economy segment, while you eat the premium hotel's lunch.