Need help getting iTunes stuff off failing iPhone 4.

I'll try to keep this as concise as possible. I have an iPhone 4 that was in use until I upgraded years ago. Apparently this is the only place left that has my bands demos/recordings on it. I was unable to log into my Apple account on it, so I just set it aside and forgot about it. Now I want to try to get the songs off it, but it's so old now that it can't be recovered. It has to be plugged in all the time(avoiding ban words), so I am afraid it's corrupted. I tried to update the software, but it tells me I have to do a factory reset. I don't want to lose the songs that are trapped on it. Is there a way to get them off? I did get access to the Apple ID again, so I do have that issue solved.