Yep.

If you can keep the heart intact but take out either a main vessel or lungs the heartcontinues to pumpblood but out ofthe holes rather than to the brain.

If you take out the heart then the blood simply drains out of the body instead of being pumped out of the body.

Think about a water pump with the same hose attached to the inlet and outlet thus making a closed loop like our circulatory system. If you punch a hole in thehose the water will go spraying out every where until there is no more water to spray. If you bust a hole in the pump the water will simply drain out.

Which one would take longer to deprive the brain of oxygen?

Here is an example of what I believe is a blood vessel shot off the top of the heart of a main vessel in the lungs.
http://vids.myspace.com/index.cfm?fuseaction=vids.individual&videoid=2 690954