Leeching neighbor's WIFI for disconnect protection

[Shanemex]

I live in a suburban area where there are not many houses very close together. There is only one open WIFI router that my computer can detect, but the signal is very weak and sometimes doesn't show up at all. When I try to connect to the router, it is so slow that I can't really do anything, although I was able to determine that somehow they have verizon DSL, when it is not available for me. I have two cable modems, but they are both from the same company, so when one goes down, they both go down. I need some type of backup, but I can't find any other ISP besides dialup that is available. I normally 8 or 10 table SNGs, so disconnections are extremely costly. Even though I play relatively low stakes, a ten minute disconnection last night cost me over $200.

Is there some way I can boost my connection strength with my neighbor's router, preferably something that I could do without involvement on their part? Are there more powerful antennas or signal amplifiers that will help?

Thanks