If I wanted to do what you are suggesting (and I have, several times), I would use another computer you trust to work well. Install unetbootin. There are is a Windows version. Download the disk image (ISO) for the current version of Linux you're considering. For an older machine, I'd recommend Lubuntu. Use unetbootin to create a bootable USB flash drive if your target machine can boot from USB, or burn the ISO to a CD if not. Boot from the USB or the CD. When Lubuntu loads, there should be an "Install" icon on the desktop.
WARNING: Installing any Linux distribution over your old windows will wipe all data unless you choose a dual-boot configuration, but since you can't clean the Windows, it sounds like that's exactly what you want anyway.
There's a bit of a learning curve moving from WinXP to any Linux, but not as great as moving from XP to Win8! Lubuntu is pretty easy, a good jump from XP.
I currently run Ubuntu 12.10 on a new Acer notebook, on my wifes 10 year old desktop, my younger daughter's Acer netbook, and on my older daughter's Toshiba notebook.
I run Lubuntu 12.10 on an old EEEPC-900 netbook hooked up to the stereo to play Spotify throughout the house, and on an old salvage-build tower in my classroom to run my python-whiteboard. Lubuntu is my clear choice on old equipment!