I have, I dunno, maybe 600 or 700 songs spread between my computers and my (rather old) iPod, not all of which is actually loaded into iTunes (more than once I've downloaded a band's entire discography and never got around to listening to more than half of it). If you include all the physical-media music in my house -- not much of it technically belongs to me, but I like a fair amount of it and listen to those records pretty often -- you could throw in another couple hundred songs. I have very little little idea how long that would be, so I'll go for "several days". Probably not dead, but in bad shape.
Counting the MP3s and the vinyl/CDs separately would be pretty redundant, though.
Actually, if you include my Rock Band songs, I think it'd jump by another couple hundred (there's a fair amount of overlap but I have all three of the main games plus Lego Rock Band and a smattering of DLC; that's like 250 songs or something). And I do often use Rock Band 3 as a music player, so including it would be fair.