I was having the same issue on OS X 10.9.3 with Firefox 30.0 after the upgrade to Firebug 2.0 from 1.12.8. Clicking the Firebug Button produced no results (no error messages, no launch).
Checking the /var/log/system.log for firefox references yielded a ton of these two messages (obviously with varying memory locations listed in each occurrence) after simply launching Firefox and doing nothing more:
6/12/14 1:07:39.000 AM kernel[0]: Data/Stack execution not permitted: firefox[pid 9790] at virtual address 0x1063df000, protections were read-write
6/12/14 1:17:32.000 AM kernel[0]: process firefox[9790] caught causing excessive wakeups. Observed wakeups rate (per sec): 151; Maximum permitted wakeups rate (per sec): 150; Observation period: 300 seconds; Task lifetime number of wakeups: 74214
6/12/14 1:17:34.470 AM spindump[9899]: Saved wakeups_resource.spin report for firefox version 30.0 (3014.6.5) to /Library/Logs/DiagnosticReports/firefox_2014-06-12-011734_pmpmbp.wakeups_resource.spin
6/12/14 1:31:22.000 AM kernel[0]: firefox (map: 0xffffff803d5415a0) triggered DYLD shared region unnest for map: 0xffffff803d5415a0, region 0x7fff8ae00000->0x7fff8b000000. While not abnormal for debuggers, this increases system memory footprint until the target exits.
6/12/14 1:40:41.792 AM firefox[10038]: -deltaZ is deprecated for NSEventTypeMagnify. Please use -magnification.
These repeat a number of times. I remembered having a similar problem after I upgraded to 1.12.8, and thankfully was able to remember what I did to fix it way back then as well. In that instance, I had an old plugin that was no longer being maintained and had remained in my Internet Plugin's folder from the previous version of Firefox after upgrade completion. After removing the old plugin and restarting Firefox, I was able to launch Firebug without issue at that time.
Fast-forward to tonight with FB 2.0, and the same problem again. I have no idea which of the following three plugins was at fault this time, but after doing the following maintenance to remove plugin's I hadn't used in a long time and restarting Firefox, I was able to finally launch FB2.0 and everything works as expected. Note that simply "Disabling" the same 3 plugins listed below via Firefox's plugin management page didn't have any impact, I had to remove them from the Plugin directory.
497 rm -rf XATTConnectEventEntry.plugin/
498 rm -rf XStamps.com.plugin/
499 rm -rf XExif\ Everywhere.plugin/
So it may be worth it for you guys hitting this problem to try removing yours one by one until you hopefully hit whichever is causing the trouble for you.. This might not actually be your problem given you're on Window's though, so I provide no guarantee of success using this method. :-)