Okay, as a relatively young guy that's pretty well to-do about IT stuff; I'll give you an opinion.
The PowerConnect 2824 is a Gigabit Switch, that's about the best switch you can expect in a home deployment, unless you have a specific need or specialty, then the PowerConnect 2824 is very adequate. I've seen these switches at small-ish businesses, and I've been very pleased with the PowerConnects. AFAIK, these do not run in a HUB mode. I don't know of a managed switch that does. If you look at the switch for a minute and observe the activity patterns, a HUB will relay all packets out all ports (except the port it came in on) which will cause all lights to blink at once. If at any point, pairs of ports are blinking independently of the rest of the switch, then it's switching, and not in a "hub" mode.
A quick explanation (since the other was vastly inadequate): Hubs forward everything everywhere, Switches, switch packets only where they need to go (hense the name), routers, move things around based on IP address. Switches are vastly superior to hubs because they don't consume bandwidth on every port for every connection (only the ports involved use the bandwidth required to move whatever data is going around) - routers, due to the complexity of their tasks, generally move fewer packets around than switches, per second; given that your internet probably isn't as fast as the Gigabit switch you're using, this is probably just fine.
To further clarify with your RT56u, it has a switch built in; all "LAN" ports are switchports. The "router" isn't doing any significant routing. Usually, the wireless data connections, are switched to the LAN ports (where the management side of things, which controls the wireless mode (AP, Adhoc, etc), channel, passphrase, encryption schemes, etc. is usually sent to the CPU for settings). - this means that wifi to LAN may be faster than WAN to LAN.
Anyways, definitions aside, if you want another DHCP server, set one up. no worries there, I'd suggest looking up the manual for the Powerconnect and resetting it to defaults. If you don't have an IP for it, and a login, I don't know how you would determine that information (besides using the console... did that version have a console?). Following the factory reset procedure is a good bet.
Word to the wise, if all the lights on the Powerconnect are blinking all the time, just a constant blinking, you're likely experiencing frequent broadcasts, which could be a "broadcast storm", and might indicate a faulty device or switching loop, which is reducing your overall bandwidth. Unplug everything, and slowly plug things back in, one-by-one until the condition reoccurs, when it does, trace the most recently connected line, and determine what that device is doing to create the storm.
if relocating the RT56u would improve signal, you can connect anything else that's plugged into it, into the PowerConnect, and move it anywhere in the house, just plug any home-run line, into the LAN connection on the device, and it should continue to work exactly how it always has.
The RT56u is already a WAP. by default, it's bridging the WLAN to the LAN; so do whatever you'd like with that, and treat it as a WAP. just don't plug the uplink to the rest of the network into the "internet" side. Make sure your DHCP response includes a default gateway which has a connection to the internet (I presume this is the UVerse Modem).
overall, I don't think you're too bad, provided you have no switching loops, it sounds like you just need to relocate your Wifi AP; and I don't think there are many, if any barriers to that.