First, you really won't need to make a starter when re-using a yeast cake. The point of a starter is to grow the yeast population from a purchased pack or vial up to the point where you have 'enough' cells to starte a healthy ferment. You could say that your previous batch was just a really big starter in itself, you have plenty of cells already. What most people do in this case is just brew up a new batch of similar beer and then rack the new wort right on top of the old yeast cake.
A rule of thumb here, you always want to do this with either the same recipe as your yeast consumed originally, or a generally bigger/darker/stronger recipe to mask any flavors that might transfer over from the yeast trub. So using the yeast from one IPA for another is great. You could use the yeast from a bock style beer for an amber, but you wouldn't want to use the yeast from an amber for a pale.. for example.
If you do this, I'd suggest trying to brew the new batch and get it on top of the old yeast cake on the same day. It sounds like your yeast should be fine to try this with tough even on the third or fourth day. Some people will intentionally leave a few inches of beer on top of the cake to keep it hydrated for a day or two be fore doing this. When you are ready, just pour off any remaining beer from the previous batch and rack your new wort in.
The other method I think you were eluding to is harvesting and washing your yeast. This is when you take a small sample of your yeast cake and 'wash it' save it for later. I've done this a few times with small mason jars when I had a unique strain of yeast I wanted to save. It works well but is a lot of effort. You can read up on this method here http://www.homebrewtalk.com/f163/yea...strated-41768/
Best of luck!