Thanks bigpaws. I'm using the crossover cable. It worked with WinXP*, so the Optiplex 755 computer can connect.
Well, I tried the beta release of 7.1, and was unable to connect to the internet, so I'm back on the noisy computer. I installed it using "automatic", and it wiped out the copy of WinXP that the guy at the store set up in another partition (which frankly doesn't matter). It barrelled ahead and formatted everything into one partition -- it didn't even create a swap drive. Yeesh. Then in trying to connect to the internet, I ran "pppoe-setup", which told me that I'd have to install "pppd" before it could set me up. I noticed that vasm no longer has a firewall set up utility, and so instead I would have to rely on gufw -- which only seems to set up rules for amule or qtorrent or various other programs that aren't installed. I also noticed that vpackager was missing in action. Hmm.
I then tried Arch, but it just kept saying to me, "mei_me 0000:00:03.0:reset: connect/disconnect timeout" -- it said this to me hundreds of times slowly, and like a zombie I stared at it, whimpering "please stop". This went on for some time.
Guess I'll download Debian and see. I'll have to make sure I have the program pppoeconf.
*not automatically -- I had to use a wizard to set up my username and password for it to work.