Linksys WRT54G WiFi Repeater
Unleash the Hidden Features Using DD-WRT
Overview
Linksys WRT54G router is capable of working in repeater mode with third party firmware like DD-WRT. A WiFi repeater is a device that will connect to another wireless access point and redistribute the signal. Repeaters are typically used to extend the coverage of a network in office buildings, hotels, convention halls, airports and other public spaces.
Repeaters can also be used on a smaller scale to share an internet connection with a neighbor. You can also use a repeater to set up a communal open hotspot and share the connection with a group of neighbors.
Installing DD-WRT
As of June 2007, DD-WRT beta v24 firmware is the only version that works in repeater mode. You can download it here.
To determine which one is appropriate for your version of WRT54G you need to consult the wiki. Some of the more recent versions of WRT54G have a RAM issue that can be overcome by installing the smaller "micro" version.
DD-WRT firmware is relatively easy to install and setup. The installation process varies slightly based on the version of the router you have. The older WRT54G models you can buy used on Ebay are better candidates for third party firmware installation.
Linksys has moved away from open source firmware in the new models of WRT54G. However, the current WRT54GL will still accept third party firmware. Not surprisingly, this model costs more than comparable units so stick to the used stuff when you can.
Source
Tutorial
The first thing to check is to make sure you're using WPA2 (a.k.a. "WPA2-PSK", "WPA2-Personal", "WPA2-Enterprise", "802.11i with AES-CCMP") encryption if you're using encryption at all.
The 802.11n and 802.11ac standards both require AES encryption because the older wireless encryption types—(WPA (TKIP), and WEP) can't keep up with N and AC data rates. If you don't configure your AP and client for AES, you'll be forced to 802.11a/b/g rates, which max out at 54mbps.
If that's not your problem, then it could be that your client is far enough away from the AP, or there's enough interference on the channel, that the signal-to-noise ratio (SNR) is so low that N and AC rates aren't maintainable, so it's using A/G rates by choice. If your software can show you your SNR in dB, or your separate signal strength (RSSI) and noise in dBm, then update your Question with that information. At the very least, RSSI in dBm is a hugely important measure in any discussion of Wi-Fi rates and range.
Also, your roommate's router is a simultaneous dual-band router, and your client card is capable of using either band. Did you say that you're seeing the same 54mbps cap in both bands? Relatedly, I'm concerned about this notion of a power slider in mW that only goes up to 200. In most regulatory environments, devices are allowed to use up to 1 Watt (== 1000 mW == 30dBm). I'm pretty sure that the RT-AC66R has high-power amplifiers that allow it to reach the regulatory max, so it's weird to hear you describe UI that seems to suggest it's limited to 200mW. Or maybe I didn't understand your description of the slider.
In a separate comment, you said it would be inconvenient to move your computer close to the router, but couldn't you convince your roommate to let you temporarily move the router into your room to see what connection rate you get? It doesn't have to stay hooked up "to the Internet" for this, just plug it into power in your room and see what 802.11 signaling rate your software says you're getting.
Another tip since you're using an internal card in a desktop PC: The inside of a PC case can be an very RF-noisy environment. Hopefully your card is well-shielded to prevent receiving interference from other internal components. Make sure your card's port fence is making good contact with the grounded shielding of your PC case. Make sure your antenna leads are screwed on tight. Make sure your antennas are as far away from your PC case and monitor as possible. The most common source of Wi-Fi interference in a PC (well, besides Bluetooth obviously) is the graphics card, video cable, and monitor. Hopefully your situation won't come down to RF interference engineering within your own PC.
By the way, You do have a gross misunderstanding of 802.11; it has never been the case that connecting an older-generation device to a wireless network would drop the whole network down to that older-generation speeds. That is an unfortunately pervasive myth that has always been false. If your AP and client are AC, your AP and client will talk to each other at AC rates when either of them has something to say to each other, and the G client and the AP will talk to each other at G rates when either of them has something to say to each other. This is one of the things the Wi-Fi Alliance's Wi-Fi logo certification program tests for. Any device with a Wi-Fi certified logo on it has proven that it does not switch to older-generation rates just because an older-generation device has joined the network.
Best Answer
It should be possible to use two routers to work-around this problem, assuming you know your WPA Enterprise login credentials, or have access to them where they're stored on your PC. (Or even a single access point with multiple radios, but the setup is probably more complex.)
You can use one router to connect to the WPA Enterprise network as a client. See this
Then use the second router to host a network that shares the first router's connection using NAT.