[sesolcSTI]

When you remove the handle and take out the ball-stem piece there should be some little rubber cups inside (not inside the ball, down in the body of the faucet) with little springs behind them. You can dig them out with a small screwdriver or a bent paperclip or whatever will snag them out of there, make sure you get the springs out too. If these cups go bad the faucet will leak. If its a popular brand of faucet, moen, delta, etc. You should be able to go to home depot and get a replacement kit to for the cups/springs.

As far as getting hot water out of your cold side, this could also because of those cups inside. If not, check your angle stops under the sink (the little valves that turn on/off your cold/hot water).

Ive been in the field for 10yrs, although 80% of my experience is with exterior stuff, if im way wrong then ask 95nracer.......I'm sure he knows interior stuffs more than me.