I have been trying to book a flight from tel aviv to eilat for april 2010.
I cannot procede either from kayak's website, or arkia, or israir.
Can anyone tell me how to do it?
I know that there are flights from tel aviv to eilat, but how do you book them?

Also how far is ben gurion airport from tel aviv and what is the cab/sherut cost?
how far is sde dov airport from tel aviv and what is the cab/sherut cost?
what is the cost from ben gurion airport to sde dov airport and what is the distance?
Much thanks

Sde dov is IN Tel Aviv, so the taxi should be 50-60 sh (15 $) . Ben Gurion is 15 Km far from Tel Aviv, probably the taxi will be 150 - 175 sh (~ 40 $). The price depend on the time (day, night, holiday).

I do not know why you can not command tickets online. There are sites that require to be registered.

I've no idea either. But, we flew from Cairo-Tel-Aviv-Istanbul last year and even our travel agent had to use another agent in Israel to book these flights. It took awhile. It may be a security thing. Try emailing a travel agent in Israel, or finding an Israel specialist travel agent where you live.

I just did a search on Kayak for flight TLV/Eilat and up popped Israir flights, two of them @ $170 return. Apr 14-19. One morning flight, one evening flight.

Kayak site showed you can book these thru Cheap Tickets or Orbitz. Total fare with the tax came to $180.

Try the Arkia or Israir web sites directly. They usually offer the best deals:
www.arkia.co.il
www.israir.co.il

Regarding getting to Ben Gurion airport, there's also the train option. They depart from either Arlozorov or Ha-Shalom stations.