Actually, it wouldn't take very much at all... just simply upgrading your videocard and installing one with TV-OUT.
That HP Pavillion does not have an AGP slot, so you are limited to a PCI videocard. What you also get is a much, much better 3D card in the process as just about any aftermarket videocard will be LOADS better than the internal integrated intel video.
While badly obsolete by today's 3D standards, I'd recommend an ATI Radeon 9250 PCI. I recommend this card specifically because it's TV-Out, Theatre Mode and dual-display drivers are very, very easy to setup exactly what you are trying to do. Here's one, retail box, with the cables you'd need for $56:
http://www.newegg.com/Product/Product.asp?Item=N82E16814131284
Installation shouldn't present too much of a problem. The only tricky part should be getting the on-board video disabled, so you may wish to check the BIOS or manual first to see how difficult this may be. Sometimes a BIOS update is needed but unsure for that particular model.
With the above videocard, the ATI drivers allow you to configure a second monitor using the TV-Out port either with a composite RCA-style cable (included) or svideo cable (if your TV has an svideo input). You can also set a nice "Theatre Mode" which will allow you to use your desktop for windows on your monitor while a DVD or streaming video outputs to the TV-Output. It's very easy to use, configure and install. For games, you would simply set "Clone Mode" in the drivers and game output will be mirrored- which sounds exactly like what you want to do.
Oh, and kudos for caring for your wheelchair bound mother. It's a very nice gesture. :grinthumb