Ok, there are a lot of things to consider based on your girl's needs. Essentially, this is almost mandatory, if she doesn't already have one get her an external hdd so she can atleast back-up all her work. If you don't have one, at the very least have her burn important files regularly to dvd or cd for emergencies. It seems a lot of work but if you've ever had a major pc meltdown you'd know the true value in this practice. Second, the computer. I don't like the battery issue, that's unacceptable and i don't know that it is the bios causing that. It could be the battery itself, maybe replace it if necessary but as long as it's just that lil annoyance, well, i wouldn't feel comfortable. It could go out on her at the most crucial of moments; uncacceptable.
The bios, i actually flashed a friend's notebook's bios when i had it in for re-install in my spot. It sounds like you purchased it recently so i'd check the oem's site asap for a bios. You only need to update to the latest version, it has all the fixes of the previous. Interestingly enough, i believe his was a 1501 as well

..hehe, small world.
...google'n...
ok, turns out the battery message is the bios. There's a bios upgrade available that fixes this specific issue. I'd get it soon as possible.
http://support.dell.com/support/downloads/download.aspx?c=us&cs=19...p;l=en&
As far as ram, being Vista..i'd highly recommend 2gb... especially being a notebook since they're known to share system ram w/ the GPU (video card). i'd also look for whatever updates you can get while at Dell's site.
http://support.dell.com/support/downloads/driverslist.aspx?c=us&cs...&l=
^^ make sure you change it to Windows Vista, default is Windows XP.
k. good luck.