Recently I left my N900 running to long and the battery died completely. When I tried to charge it, it got into a reboot loop for about 6 hours before I unplugged it and it then booted normally. However, much seems to be wrong with it. Trying to launch the camera app or play a song with Media Player gives me an error that "Audio is in use by another application" even when no other applications are running. The phone seems to be locked into speaker mode. Alarms make no sound (these all seem related). But also, my IM accounts no longer connect, and my email won't load new messages. Web pages don't load either (both on wifi and 3G). Apt-get and FAM hang when updating the package list and HAM just hangs. Finally, the notification light no longer shows anything (I had a custom idle pattern in there).
I think the only solution is to reflash. However, I want to preserve all of my data, and if possible all of my installed applications. How do I do this? I really don't want to lose anything unless I absolutely have to.

Try installing and running Backupmenu. I don't know whether it will preserve your problems too, but it's worth a try.

Unfortunately, as Internet isn't working, and neither are any application managers, I don't see how I can do this.
Is there a way to simply copy my entire emmc to a file on a computer? I certainly have 32 GB free. Would this preserve my applications, or just my files?