2007 Caliber; My 1 ton paperweight
 

Help? My problem is not reflecting to the check engine system. SOO, I can't get it checked for a code. So i am scared to get more parts, and that not even be the problem.
It was dying when going a slow speed, or stopping. Some shuddering. WAS throwing the Throttle Body and Oil light. Anyway, here's what we have done:

Oil Change.
Replaced the Throttle body.
Replaced Cam Sensors.
Went to the dealership for a computer software upgrade & was told it is up to date, none needed.

The dealership fellow said he suspects the fuel pump based strictly off of driving it.
Well, I drove it some because it was needed, with the Christmas holiday and work.

Now it won't turn over all the way. The oil light will occasionally come on for a couple seconds then go right back off. You can hear the pain in the engine when trying to start it.
any ideas?
No electrical problems have presented, I recently replaced the battery also.

Will it start with a jump?