Maybe a bit stupid, but if your A drive doesn't work anymore you could try to compress everything with WinZip and then email it from your old computer to an email account and then later download it with your new computer....
Depends ofcourse how much you have to copy, how muchspace there is on your emailserver (usually around 10 MB) and how much a local call costs.
Good luck !
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¡ Yo quiero Taco Bell !