I had problems with my desktop displaying it with the TV, would work grand on a small monitor, but with TV it would start OK as it booted then go blank, however it was running windows 7 and when windows 10 came out some how it managed to get windows 10, at which point it worked A1 with TV, so clearly something to do with operating system not the PC.
With this in mind you may find another operating system works better, since most TV's work on Linux I would guess a Linux operating system would work better than Microsoft, clearly you don't want to get rid of XP, however you can get, often from mag get give away Linux live CD's which allow you to temporary run Linux, I used them to access files with Microsoft passwords, if you can get hold of one of these CD's then that may be the easy cure, and also show if the problem is hardware or software related.
I have never been a Linux lover, daughters old boy friend had these CD's and tried to convert me, and failed. I also use programs like Photoshop and Gimp with Linux just does not work as well, but to pop in a live disk to test if operating system or hardware problem seems a simple and cheap way forward.