I hope you kept a copy of your 4.9 installer just in case.
The bouncing dock syndrome is generally a Java issue. However, you can repair permissions before just to check. Reboot whilst holding down the SHIFT key until you see a window saying Safe Booting. Then after it has started up, go to Utilties folder & open Disk Utility. Then Repair permissions. Then reboot normally & try LW again. Any difference? If not, reinstall Java using the "Offline" installer:
http://www.apple.com/downloads/macos...update142.html
This one usually does the trick but there's another java security option if it doesn't. Java for osx often installs badly or the initial online version has bugs.
I would also recommend deleting your LW preferences after installing Java & before opening LW. LW prefs are found here: /Users/your_username/Library/Preferences/LimeWire & delete the entire folder. Then try opening LW.