Hi Micah, output below.  However - it looks like the breakage is due to profile issues.  
firefox -ProfileManager, and creating a new profile worked.  I was able to copy my old extensions directory to the new profile, and all the extensions worked on the new profile.  Also tried removing XPC.mfasl, XUL.mfasl etc from my old profile dir. - no luck on having the old profile directory work.  So I tried restoring my old profile directory from a backup; trying to launch produced this message: 'Malformed File: Firefox could no install this item because "install.rdf" (provided by the item) is not well-formed or does not exist. Please contact the author about this problem."; after clicking ok, it started with what looked like blank profile.

$ COLUMNS=200 dpkg -l firefox\* xul\*
Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Cfg-files/Unpacked/Failed-cfg/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name                                         Version                                      Description
+++-============================================-============================================-========================================================================================================
ii  firefox                                      3.6+nobinonly-0ubuntu5                       safe and easy web browser from Mozilla
un  firefox-2                                    <none>                                       (no description available)
un  firefox-2-dom-inspector                      <none>                                       (no description available)
un  firefox-2-gnome-support                      <none>                                       (no description available)
un  firefox-2-libthai                            <none>                                       (no description available)
un  firefox-3.0                                  <none>                                       (no description available)
un  firefox-3.0-branding                         <none>                                       (no description available)
un  firefox-3.0-gnome-support                    <none>                                       (no description available)
un  firefox-3.1-gnome-support                    <none>                                       (no description available)
rc  firefox-3.5                                  3.6+nobinonly-0ubuntu5                       dummy upgrade package for firefox-3.5 -> firefox
un  firefox-3.5-branding                         <none>                                       (no description available)
un  firefox-3.5-gnome-support                    <none>                                       (no description available)
un  firefox-3.6                                  <none>                                       (no description available)
un  firefox-3.6-branding                         <none>                                       (no description available)
un  firefox-3.6-gnome-support                    <none>                                       (no description available)
un  firefox-adblock-plus                         <none>                                       (no description available)
ii  firefox-branding                             3.6+nobinonly-0ubuntu5                       Package that ships the firefox branding
un  firefox-gnome-support                        <none>                                       (no description available)
un  firefox-granparadiso                         <none>                                       (no description available)
un  firefox-granparadiso-gnome-support           <none>                                       (no description available)
un  firefox-libthai                              <none>                                       (no description available)
un  firefox-trunk                                <none>                                       (no description available)
un  firefox-trunk-gnome-support                  <none>                                       (no description available)
ii  xul-ext-adblock-plus                         1.1.3-1                                      Advertisement blocking extension for web browsers
un  xul-ext-thunderbird-locale-en-gb             <none>                                       (no description available)
rc  xulrunner                                    1.8.1.16+nobinonly-0ubuntu1                  XUL + XPCOM application runner
rc  xulrunner-1.9                                1.9.0.14+build2+nobinonly-0ubuntu1           XUL + XPCOM application runner
un  xulrunner-1.9-dbg                            <none>                                       (no description available)
un  xulrunner-1.9-gnome-support                  <none>                                       (no description available)
ii  xulrunner-1.9.1                              1.9.1.8+build1+nobinonly-0ubuntu1            XUL + XPCOM application runner
un  xulrunner-1.9.1-gnome-support                <none>                                       (no description available)
un  xulrunner-gnome-support                      <none>                                       (no description available)