I finally got it fixed....somewhat. Not really sure what fixed it, but it's working.
I had downloaded the latest driver from ASUS's website, and trying to update the driver in device manager, which told me that I had the latest driver, but I ran Windows Update and it found a later driver, so I installed that. This, didn't fix things. In fact, it made things worse for a while. After doing that, every time the computer restarted, I had no internet access, so just rebooting wasn't a solution anymore. Sometimes, disabling the network adapter and then enabling it gave me access. I tried rolling back to the old driver, but the new problem of every boot-up remained.
I started to suspect maybe there was a hardware problem, so I tried different ethernet cables but that didn't help. I tried by-passing my router and just going straight from the cable modem to the computer, but I actually couldn't get internet access AT ALL that way, I'm not sure why. But, I'm pretty sure the router is fine.
After trying to by-pass the router, I hooked everything back up like normal. I put the latest driver back on there (the one I found on Windows Update), I reset my modem, then unplugged my router and plugged it back in, and it's worked almost 100% since then (for about a week now). The only problem is, if the power goes out while the computer is on (which happens somewhat often where I live, twice this week alone) then I lose Internet access. The first time it happened, I unplugged the modem and plugged it back in, followed by the router, and it went back to normal, even after re-boots. The second time it happened was this morning. I tried just doing the disable/enable method and it worked at first, but, I haven't seen what it does after a reboot.
Any idea what's going on here? Just a crappy driver and I need to hope for a better one in the near future? That's really what I think it is.