UPDATE: I sat down with my grandma last night and explained to her how it is unsafe to use this OS. I then went on about security and she should not put any personal info on the internet with this computer. I said I do not want her to become a victim of identity theft. I tried to convince her to bank with her new iPhone.
She said she is not changing her habits. She is going to live without her 50 some songs on her iPhone. She likes how ME looks and does not want to learn something new. She said she understands that technology is moving forward, but she's happy where she is at. So that pretty much wraps up my dilemma. I'll just hope that she continues to be safe in there.
Knock on wood, she hasn't had a problem in the 13 years she has been using ME with her finances.
What I would do is grab an old junker Windows laptop, or hell a Mac. Just something that will run XP. Put it in Classic mode and ask her to use it. Don't force it, just ask her. Let her try it out. If she doesn't like it, fine. She knows the risks of running an outdated OS on the modern web now, so I'd hope she would at least be a little more careful.
I would also try the same thing with OS X. It can't hurt to try it on someone else's computer, right?
I also understand that she paid $2500 for that machine back in 2001. Judging by Microsoft's Sys Reqs for XP, that machine should do fairly well (hell, I know someone who managed to get Windows 7 installed on PIII. Don't ask me how, but I have screen shots to prove it, didn't run well).
She has to realize she is trying to sync a device 12 years newer then the machine she has. It is also faster, with double the RAM and 64-bit processing.
I know XP is unsupported, but more apps support it right now then probably any did with ME. Plus, XP is hailed as Microsofts Best OS ever, with 7 in a (very, very, VERY) near 2nd.
She also has to realize that she bought the machine in 2001. 2001. By todays standards, that machine is a dinosaur. It has gotten her this far, but it won't go much further.