UPDATE: A while after this fix, it stopped working again. I gave up for a while, but recently, we got a new modem, so I tried to connect again, but I'm having the same problem. The only details that have changed are:

4. Hard Disk space available? = 4.31 GB
6. Modem & router brand name & model numbers? = Webstar Modem, Netgear WGT624 v4 Router

Everything else is the same, except Java 1.6 may have been updated (specifically, it's 1.6.0_11, but I'm not sure if it's been updated from the first time I posted).

Any help would be appreciated.