The main issue, is the fact that you've lost everything (not just one of the needed things, to recover each of those).
Is it possible my friend set up some different interface and not Blockchain's?
Is it possible I was using something besides Blockchain?
If you used an online wallet (on that time), then most likely it was blockchain.info.
Were there even interfaces like that back then?
Yes.
Is there anything I can do to try and track down my wallet identifier?
Normally, the following links should be the answer but I'm sure you've already tried everything (based on what you wrote earlier):
1.
Remind Recover Reset2.
SupportThe only other way that I can think of, is to use a recovery tool for your hard drive (don't get your hopes up).