So to summarize:
1. You're at a site with no water hookup
2. The fresh water tank under the kitchen sink is full
3. The water heater is full
4. You can disconnect the inlet tube to the pump, and suck water out of it.
5. You replace the inlet tube, and pull the outlet tube off the pump. You switch on the pump, but no water comes out of the pump outlet.
6. The pump motor runs.
If all of the above is true, then the problem has to be in the pump - specifically the pumping end of the thing, not the motor.
You probably have a Series 2088 Classic pump. Shur-Flo sells a rebuild kit that includes all the seals and membranes.
http://www.shurflo.com/pages/RV/rv_c...es/repair.html
Unfortunately, the kit seems to be more expensive than a complete new pump - PPLMotorHomes wants $77 for the kit, and $75 for the entire pump! Any RV place will have the pump, and a big RV place might have the kit. Either is easy to install.
Bill