jamgood96:
Hmmm, well that seems to work so far. I've only had a few minutes this morning to play, but I haven't gotten any failed attempts (except for when I forgot to change the IP).So what's different? Why is this one connecting fine whereas the others weren't?
The others were not mine. 
edit: There are some reasons mine works better. I know how tcp works. If you look at the getPage() function, you will notice the "while(client.connected()) while(client.available())" loops.
If you are downloading a big page (like Google's home page), you will get several packets. That loop will check client.available(), and for a while, it will be zero. Then it will be about 1400. Your goal is to empty that rx buffer as fast as you can. Get client.available() to zero. Then it may be zero again for a few checks, then it will be 1400 again (another packet).
The client.connected() will return true until you have emptied the rx buffer of the final packet, so as long as client.available() returns non-zero, you are connected.