By default you should be able to Offer your Screen even if you have not set Screen Sharing On.
This works on the basis the firewall stops incoming stuff but not outgoing stuff.
It does seem to work better and more consistently if it is Turned On in the Video Menu > Screen Sharing (Toggle with a Tick of On)
Have you tried Toggling it Off then On again ?
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously