Pitcher #1 leaves the game with the score tied at 2-2. He leaves a runner at 2nd. Pitcher #2 enters the game and gives up that run making it 3-2 and 3 more. In the bottom of the inning we score 1 run making it 6-3. The final was 7-4. I know that MLB rules state that the team must tie or take the lead for a pitcher to be "off the hook". However what happens with the team puts up more runs than the starter gave up? Does he still get the loss?

Yes - the starter gets the loss...

To amplify 08Dad's reply, here is the applicable rule:

10.17 (d) A losing pitcher is a pitcher who is responsible for the run that gives the winning team a lead that the winning team does not relinquish.

Rule 10.17(d) Comment: Whenever the score is tied, the game becomes a new contest insofar as the losing pitcher is concerned.

By the way, my advice is to avoid any emotional investment in a pitcher's W-L record. It takes a whole team to win or lose a game, and that's the record that matters.

It doesn't matter if the team scores more runs than the pitcher gives up. He was responsible for the go ahead run, so when he left the game (techincally not literally) they were losing by 1. The team never tied or took the lead in the game so he would get the loss.

Starter gets the loss

He was responsible for the guy on base.