Cannot start Thunderbird.exe 1.5.0.9 (20061207) from the PortableApps menu

that Thunderbird Portable is not to be started with the exe you used (\PortableApps\ThunderbirdPortable\App\thunderbird\thunderbird.exe)!
If you use this exe, portability is lost and stuff is left in the PC you use it on.
If you start it manually, use the \PortableApps\ThunderbirdPortable\ThunderbirdPortable.exe

There's something wrong with your profile. Your Thunderbird Portable profile is contained within ThunderbirdPortable\Data\profile. Unfortunately, it looks like it has become partially corrupted. This is why when you run ThunderbirdPortable.exe or start from the menu it fails (it's using that profile) but when you run thunderbird.exe directly it works (it's using a local TB profile from the PC of there is one or creating a blank one if there isn't).

Make a copy of that profile folder to somewhere else then delete what's there. Start TB Portable from the menu or TBP.exe. It should start fine with a blank profile. Close TBP. now try copying in bits from your other profile. Things like your mail folder, etc, one piece at a time. The usual culprit is the prefs.js or an extension. So copy in the prefs.js second to last and extensions folder and extensions.rdf, etc last. Be sure to restart in between each copy to ensure it still works. If this is more than you're comfortable with, ask a techie friend to assist you.