A. Caspis wrote:

Before I call it quits I want to try one more thing: reflow the PCBs.

What make & model laptop? HP by any chance?

Find a company with the equipment to remove and replace BGA packages.
They will have to be replaced with new chips though.

Here is a description of a rework station ...
http://www.digifixltd.co.uk/articles.html#anchor

and a UK company who offers a service (but not in the laptop field)
http://www.sers.me.uk/ic_fitting_service.htm

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Adrian C