You said you have Sprint, so that would be 1900 MHz. The intermediate frequency being sent down from the dish to your receiver can interfere with that band very slightly. It's not exactly in the range but it's close enough to cause trouble especially since you said your cell reception is weak to begin with.
The dish needs to be looked at, and especially the connections, for poor fittings or frayed wiring.
If everything looks okay then the dish should be moved away from where you intend to use your cell phones.
Failing all this, consider buying a cell phone booster with an external antenna that you can put on the roof.
I have to agree, being a ham radio operator, sounds like a bad connector thats leaking RF. Check all connectors and cables. Another remote possibility
is the length of coax being used is radiating on a harmonic of the IF frequency.