Not sure what the UAII assembly process is like, but Project Arcade suggest that in addition to the screws used to assemble your cabinet, wood glue can (and probably should) be used to increase stability. You could probably glue the UAII in the same general places that Project Arcade describes if you're worried about it. Of course, that means you can't take it apart in the future.
All that being said, 2 months ago, I was in the exact same boat as you. I owned no tools, had never worked with wood in my life (what's a router?), and had an intense desire to obtain a cabinet to house my mame computer. None of that has stopped me from attempting to build my own from scratch.
I finished my cuts Sunday morning and am almost ready for assembly (just need to route the t-molding groove) and I have to say things have gone extremely well. Granted, I have taken things VERY slow and researched a ton before moving ahead with each step, but it has all been a lot of fun and I've learned a lot. The "Search" function on this forum is actually the most useful tool you can find. It seems like any problem or question you will run in to has been dealt with on here before. Sometimes, the hardest part is finding the answer buried within all the info on here.
As for not owning tools, I was suprised at how willing people are to let you borrow. I am a huge gamer, and rarely have common "man stuff" to talk about with my peirs, but it turns out that woodworking is a pretty common hobby for a lot of guys. A lot of times, you simply have to ask them "Do you do any woodworking?" and you've opened a door to all kinds of advice and tools they can provide you. I've got a saw, router, and jigsaw from 3 different people. I didn't have to ask to borrow any of them (they offered them all before I could ask) and they told me I can keep them as long as I want (or until they need them for something).
As for getting the wood home, I found out that Menards and Home Depot both sell the sheets you need, and at both places you can rent a truck for 19 bucks to bring it home. They will even help you load it onto the truck. You just need to go bug you're neighbor to help you unload it. As for moving it to you're gameroom after it's assembled, yeah, that's something I'm worried about too. I'm considering assembling it in my basement where it's going to live, but I'm wary of the dust that occurs during sanding in between coats of paint. Oh well, when the time comes to make that decision, you can bet I'll be on here to see how other people have dealt with it.
All in all, I too was considering a UAII cabinet and am glad (so far) that I decided to build. I've save a lot of money and am learning a new craft, so it's really a win/win.