I would agree with Lilith and Sharni, this sounds like a software problem not hardware. It's not like the PC is crashing all the time, the mail program she is using is either not working properly or is misconfiured.
I would start with checking all the settings for the mail software that she is using and make sure that things like "leave message on server" are not checked, if they are no matter how many times you delete it locally each time you check it downloads it again. This is not a likely cause, as she would just fill her inbox up quickly and stop getting new mail... but it is worth checking.
The other thing I would see is if the mail access she is using (be it her own ISP, Yahoo, etc) has a web based interface. She can check her mail using that for a little while and see if the duplicate messages just keep showing up (maybe the oher end has a virus that is sending lots of messages?) there. The other thing is that she can try to e-mail you from there as well and see if the result is any different. If it works from a web based interface then it is the local software, if not then it might be the user
While I know that there are some around that do not like Dell machines, my luck with them has been very good. I do not care for the performance of their "economy" line of PCs but I have found them to work rather well right out of the box. We use hundreds of them at work. And if you spend the big bucks for their really high end boxes they are really nice workstations.