Your potato PC fails to load games, especially after a new patch?
Try disabling SuperFetch on Windows Vista, 7 or 8.
My PC isn't that great but can run League without problems. But the last couple of patches I've got problems with games not loading for several minutes ("connection error, check firewall").
One thing I've noticed is that the svchost.exe process was constantly moving several GB of data of other games on my hard disk, apparently caused by the SuperFetch service, even if I didn't start those other games today.
SuperFetch is not bad per se because it should speed up the starting time of programs you use often by preloading them. However my suspicion is that after League updates SuperFetch doesn't recognises League any more as a program you'll use often, and so is more concerned with moving several GB worth of other games over and over on your hard disk which slows the loading process of league to a point where you'll get a timeout error.
I'm not an expert, but since I've disabled it my league games ever loaded without problems so far and my hard disk is not constantly working all the time. If you've got similar problems with games not starting it might be worth giving a try.