Thanks for the suggestion. The Acer Aspire One has plain old Windows XP Home Edition on it; nothing special like a Linux install or anything. I tried changing the wireless channel to both 1 and 11, but neither solved the problem. I also tried setting the wireless bandwith from "Auto" to "20MHz Only," but again it did not work. After that I changed the 2.4GHz mode from "Mixed" to just "G-Only" (the netbook only supports 802.11g anyways) but this also didn't work.
However, I was able to solve this problem earlier tonight, though I am not 100% happy with the solution. The problem seems to be the security settings. For whatever reason, the Acer Aspire One simply connect to the Linksys E4200 using ANY security. I tried WPA-Personal, WPA2-Personal, the WPA/WPA2 mixed mode, and WEP. All failed to actually connect to the Internet. As soon as I turned off all security for the 2.4GHz band, it connects perfeclty (and very fast, just like it should).
Now, I know for a fact that the Aspire One netbook can support secure Wi-Fi connections, because it was connected to my old D-Link DGL-4300 router using WPA2-Personal just fine. I'm not actually blaming Linksys/Cisco for this though, as it could still easily be the fault of the Aspire One (it is a two-year-old netbook after all, and we all know netbooks use the absolute cheapest components available), but people who own crappy netbooks should be aware of this issure. This specific Aspire One uses the Aheros AR5007EG Wi-Fi chipset, for future reference. And before you ask, yes I have the newest drivers installed for it.
Not having any security is obviously not desirable, but for me it's not the end of the world. I know both of my neighbors and neither of them even own a PC (they are both very, very old people lol). That leaves people across the alley way, but my router is located at the very front of my house. The signal would have to stretch across my entire house, the entire backyard behind my house, across the alleyway, across the entire backyard of the person's house behind mine, and then finally it would reach their residence. I've read the range on the E4200 is pretty good so maybe it can reach the far; I guess I have a reason to go walking around my block seeing how far my iPhone can keep a signal 
I tried using the newest drivers available on Acer's website and another set of drivers I found in a Google search. Both had the same problem. I'll keep playing around with it, but in the meantime I have a couple questions for any other Linksys E4200 owners:
Anyone else happen to have a notebook with an Atheros Wi-Fi chipset? It doesn't necessarily have to be the same AR5007EG chipset that is in the Aspire One netbook I am having problems with, but any Atheros-based chipset. And if so, how is your experience so far? Does it work correctly?
Also, anyone happen to use the MAC Address Filter on the E4200? I tried it out once on my old D-Link DGL-4200 router, but it seemed to massively affect performance. I could use it again on my E4200 as a way around not having any wireless security turned on, but not if it also drops performance by a lot. That was after all one of the biggest reasons I bought a new router 
