Can I feed power to my TripMate (or other GPS) Receiver from my Laptop's DB9 connector?

No.  There is not enough power available on the serial port of a computer to drive a GPS receiver.

It is possible to wire the laptop's 12 volt battery power over to the DB9 connector and connect it to a spare pin,  BUT THIS IS NOT RECOMMENDED unless you REALLY know what you are doing.

Joe Mehaffey