So for some reason Belethor seems to have disappeared. Whenever I go to his shop, it is locked up tight. However, when I see his assistant, he always invites me to come by the shop, so I don't think I killed him. I know there was a dragon attack in the city, but I only saw guards dead. Either way, I thought that store owners were among the NPCs that could not get killed. Is there some reason I am missing as to where he could have gone? This is also before the Civil War storyline (I haven't joined a faction yet).
Belethor is not essential (read: he can be killed), so it's possible that he's dead. I can't confirm this at the moment, but I believe that Sigurd (his assistant) will say the same things regardless of Belethor's state - he's only got about 3 lines total.
The UESP page for Belethor notes a bug that you may be experiencing, though:
Belethor's shop will often close the moment you leave no matter what the hour, and may not reopen until after his inventory resets. [...] The standard wait for reset often results in his shop still being closed regardless of the time of day. Waiting nearby in one hour increments may fix this.
I just had to wait a day for him to come back, but there are other possibilities. Check the Hall of the Dead for his coffin. Also, check out other possible problems.
You can try to use the back door, as said here. It's so much easier to play on PC because you get the Console Commands. If something happens, you could just spawn another Belethor.