I no longer have access to the email address associated with my Apple ID, so I'll need to create a new one pretty soon. All possible ways to recover my current Apple ID have been exhausted, so that isn't the issue. I'm wondering if I transfer purchased songs to a zip drive or burn them onto a CD, will I then be able to transfer them back to iTunes but not as purchased content and therefore be able to play them with my new ID? I'm not very technology savvy, so I hope this isn't a dumb question.
This is a bit of a grey area around fair use, but there is software out there that will allow you to remove the drm from iTunes songs. Given that the songs they currently sell do not have any drm, I think it's not a particularly immoral option.
If you want to stay on the clearly bright side of the law, burning the songs to a cd and then re-ripping them will remove the drm and is supported through iTunes. You will lose some quality though.