I have an old Dell Inspiron 1525 with a single core Celron 2ghz processor, 2gb ram 20gb hard drive. I just installed 13.10 on it and it runs very well.
There is one problem, however. If I try to restart or shut it down, it will not do it. The screen will go into a digital scramble/frozen look if you know what I mean, and freezes up totally. I have to hold the power button in for 5 or 6 seconds and shut it off and restart it that way.
I have done all the updates, etc that I know of, and believe me I am no amateur when it comes to ubuntu or pclinuxos 2012/2013 KDE.