First, go to www.modchip.com. Go to the PS2 subsection and look for Swap Magic v3.6 discs. Buy those ($27 with standard shipping) WITHOUT any slide card or fliptop or anything else and make sure its NTSC (if you have a NTSC PS2). Then, take some useless credit card or ID badge of the same size and shape and go to this website:
All the way at the end of the first post is directions on how to make your own slide card (don't trace it, use the measurements), how to use it, and how to use it in conjunction with the swap magic discs and backup games. In that same post (at the top) is directions on how to backup PS2 games. Be warned, that you will have to do some "adjustments" on your PS2 disc tray (nothing major, and it doesn't require you to break the warranty seal or take apart your PS2 and solder it). Post any other questions and I'll help you.
Well, I guess I won't be able to do this for a little while, my PS2 just got the DRE and I was able to get my console replaced for free (for the 4th time)