I cannot find corrupt iPhone backup file on my computer to delete it.

I have an iPhone 5s. It backed up to my computer (Mac) just fine until I got a new computer. I loaded all my backed up files onto the new computer (also a mac), from my airport extreme computer backup (also a mac product) and the next time I went to backup my iphone, it clearly says in the itunes window (where it would usually tell you your last backup date) that this phone had NEVER been backed up up on this computer. That would be fine with me and I would gladly create a new backup from what was on my phone currently except....When I click the backup button, it gives me the "could not back up the iPhone because the backup was corrupt or not compatible with the iphone. Delete the back up for this iphone, then try again" error message. I have followed every instruction of how to go about deleting these backups. I deleted every iPhone related backup through iTunes. Then I tried to find the files on the computer's hard drive outside of iTunes, but I swear there is no MobileSync folder on my computer. At least it's not at the path that is always given in every suggested solution.

I did create a separate user account (on the same computer) and was able to backup my phone through that. I don't know what that means, if anything, but I'd like my iphone to work with MY user account...

I've had a really difficult time finding the answer to this question online, so any help would be much appreciated.

Thanks!