Okay well to activate the HP recovery partition when you reboot repeatedly hit F11, or on older HP's sometimes its F10.
Look on the side of the computer, if there is a sticker with the HP OEM code I can get you a OEM disk from work and make and ISO for you. Or if you want XP, or better version of vista or windows 7 ultimate, etc let me know and I'll make ISO's on my work disks (Win7 has a dev activator so you won't need to worry about a key)
edit: For your back up do this...
http://www.villavu.com/forum/showthread.php?t=13475
Install the program, compress it all, burn to DVD, format, reinstall program, uncompress
(Before you say WTF compress?? Read the thread)