You can get various things that are used to broadcast digital TV wirelessly from room to room but I ain't sure what the connections on them are.......
You could look at this doofer if you want to do wireless video to the TV.......
Amazon.com: Video-Home 2.4GHz Wireless PC Computer to TV Video Sender and Converter - Accepts computer VGA signal and convert them into TV composite video format Wirelessly - supports VGA mode up to 2048x1536 High Resolutions: Electronics .
You should be able to set up a "twin screen" output on the laptop using it's own screen and the monitor output (hang on, you wouldn't need that since the output from the laptop alone to the TV would suffice) and then use mouse/keyboard normally with the laptop so you see everything on the big screen.
Of course, if the mouse/keyboard is the only real issue and you can leave the laptop beside the TV then do as yer told and buy a decent set.