ZLA Controller described a terrain loss of separation event when he/she failed to note the developing situation; adding no MSAW alert activated which might have prevented the incident.

Narrative

Aircraft X was handed off from Sector 10 and advised that the aircraft was requesting the GPS approach. I asked if the aircraft was my control and was told Aircraft X was my control. I selected the approach on the URETS display. When the aircraft checked on the frequency and requested the GPS approach; I gave the aircraft the altimeter and cleared the aircraft to OGSOE (IAF). I was moderately busy with other aircraft while putting in the aircraft's new route into Host. I checked the altitudes on the approach (AOA 4;400 at OGSOE) then checked the MEA chart to see if the new route would encroach the 7;000 FT MEA south of EED. When I did check the aircraft; it had already entered the higher MEA area. There was no MSAW alert prior to or after the aircraft crossed the 7;000 FT area boundary. I immediately climbed the aircraft to 7;000. Subsequently instructed the aircraft to cross OGSOE at 7;000 cleared for approach. The aircraft read back the clearance and then canceled IFR. Recommendation; If the MSAW alert worked correctly the event would not have occurred.