put in a new starter but hesitates then it starts and runs fine on 2003 Honda Element

my starter went bad, AutoZone had 2 models and they said it was either one would be okay. NOT I used the other model and the motor revved up and down real fast then I turned it off. I tried to start it again and the starter went dead so I took it back and got the right model. The starter was tested and it was good. I tested the stater wires and I got 12 volts out of the starter wire. I put the right model in attached everything correctly. When I went to start it it sounded like it was not getting gas (rough sart) and the starter sounded like a higher pitch then my old one. I tried again and it started up after a couple of ranks of the starter. Once it started it ran fine. PS., I checked before I started the Element I made sure the "Check Egine Light" was not on and it did not come on. Please HELP!!!!!!!!

Asked by for the 2003 Honda Element
Perform this test on the starter, see if you measure any voltage drop on the cables: http://www.excelauto.com/online/Tech.d/strvdt.html
Only one problem, the starter is below the intake manifold which I would have to take it off. Is there another way to get to the wires of course a honda repairman said to replace with orginal part, can I at least run it for a couple of days if I have to replace it AGAIN!!!! Thanx a bunch.