Might be that you can't access a wireless N network? Try using another mac if you have one or a wired ethernet connection to the time capsule and launch airport utility, from there see how its broadcasting, if its a older time capsule you'll be limited to your options, either N or G or both but the speed is limited.
Check these settings first, unless you got a N card in your mini you'll need a G configuration which is probably what your neighbour has as its most common.
I don't have a N carded Dell mini to know if it works with a N network as a hackintosh, but I'm sure it would.
Let me know how you get on and if you need any more help.