Yeah, people have different opinions, but if you pitch onto a whole 5 gal cake, then it's overpitching. You still need that ramp up to cell density to give you a clean flavor profile. 1/4-1/3 is about the right amount of yeast for a healthy but not too heavy pitch. If it were me, I'd wash all the yeast (pretty easy, I just use tap water. I'm crazy like that), and split it into 3 jars. Give one to the friend, and keep the other 2 for future brews. For this timeframe, washing isn't necessary.
As for the "wake up", I let it go with fresh wort for a few to several hours. It gets bubbling pretty quick.
Arrowhead, that's a strange one. 1/2 a cake in the fridge for 4 days should have no problem starting up in less than 12 hours in a new batch. Did you let them come up to room temp before pitching? May have just stressed them somehow. I bet it will start up soon. There's a lot to be said about how they were treated in the previous fermentation, like if it was a month long primary, maybe they were too dormant. I would wait a few more days and check the gravity if you're still concerned. It may just not be moving the airlock.