I would have recommended the Network Extender above, but you said your landline Internet doesn't work well, either. Sadly, without a broadband Internet connection the Network Extenders won't work, either. It's also probably easier to connect to wifi for the times the network is available.
First, have you looked at other Internet options in the area? Upgrading to FiOS or uVerse (Verizon and AT&T's fiber-based network, respectively) may solve your reliability issues.
Barring that, or just getting your ISP to fix the issues, you'll be stuck with repeaters. I have one of these for my wife's Blackberry:
Wi-Ex :: Home
It works decently, but you need to place the antenna properly. I've got mine in the attic, ran the cable to the basement, and then brought it up in the living room where the base station is. It gets me a few extra bars on Verizon and AT&T, but T-Mobile is still absent. Note that you need to play with it to figure out where you need to stand, if I'm right next to it the signal is too hot and I drop the call, if I'm 10' away it's much better.
Again, for anyone with a stable broadband connection, the Verizon femtocell solution is a much better choice:
Set Your Location