Similar to QC client with IE on a 64-bit machine, the Synchronizer really uses the 32-bit Windows on Windows (WOW) and 32-bit VC++ etc. -- This is actually a limitation of the QC Client on a 64-bit machine, not the ALM synchronizer.
So, BEFORE you load the ALM Synchronizer Server, make sure on that Server PC, that you launch IE (32-bit) and go to your QC URL as usual to get the client to load - let it install the various required elements (32-bit / x86 if given a choice), Launch IE and go into QC, login and go all the way into a project to confirm that it looks ''normal'' to you. Go back to the ''qcbin'' URL (not start_a) and run ''ALM Client Registration'' from the Add-In's page. Launch IE and go into QC, login and go all the way into a project to confirm that it looks ''normal'' to you.
Now load ALM Synchronizer Server (and client here if you wish), then start the HP ALM Sync.Server service, wait about 10-15 minutes, then try to hit it with the Sync. Client (from the Sync Server or from your own PC if you loaded it there).