Update: It appears that my problem was caused by still having the old SourceLinks/FogBugz bundle installed. I uninstalled both, rebooted for good measure, then re-installed the latest FogBugz add-on.
The FogBugz window still didn't show up when I started Visual Studio so I opened it as Administrator, confirmed that the FogBugz window was displaying, looked at the Add-on settings, etc. (Note: I made no changes) and then restarted VS as my normal user - where the FogBugz window appeared and I was able to connect to our server.
I was having the same issue as the OP, with the same setup as @Avi D. I tried the answer suggested by @Avi D and now I'm getting the following error when Visual Studio starts up:
Problem Event Name: CLR20r3
Problem Signature 01: devenv.exe
Problem Signature 02: 10.0.40219.1
Problem Signature 03: 4d5f2a73
Problem Signature 04: mscorlib
Problem Signature 05: 126.96.36.199
Problem Signature 06: 4e181ae3
Problem Signature 07: 3789
Problem Signature 08: 3e
Problem Signature 09: System.UnauthorizedAccess
OS Version: 6.1.7601.2.1.0.256.1
Locale ID: 1033
Additional information about the problem: