Do they have English "Yellow Pages" there? Try looking up marinas and yacht clubs and see if you can hire (bribe) someone to sail you to Cyprus. Seriously.
Here are some web links to marinas in Lebanon:
http://www.lamarinajk.com/LaMarinaJK_content.html
http://www.solidere.com/solidere.html
http://www.lebanondivers.com/...these guys might know someone with a boat.
The above are all in Beruit, you might check to see if there are any further north inbetween major cities that might be blockaded.
Tried that several days ago. They said that the Israeli navy turned them back when they tried.