1,000 songs is more than 2 gigs, for me atleast, but what tupac said should help you out...make several g-mail accounts maybe?
but like somebody else said, you need a burner...you really do...when i bought my comp about 4 years ago, i thought, i dont need a cd burner and that it wasnt worth the extra cost..i should go for something simple...but really, it has paid off...just buy a 5-pack of CD-RWs, and you can not only put your library on the cd, but update it everyweek or so....last time i checked, we got CD-RWs that can rewritten up to a million times...so you should be fine..
the reason im saying RW's is cuz im sure you get new songs from this board every week or so..or maybe from other places...if something bad were to go wrong, then you lose quite a bit if they werent updated on the RW...