A B737-NG Captain's FMC malfunctioned during a DFW RNAV SID causing a track deviation.

Narrative

Approaching TREXX on the CLARE 2 departure; the Captain's FMS blanked. TREXX turned white and the magenta line went away and JOLEN was no longer in the PFD map display. I attempted to re-enter JOLEN when the Captain's FMS blanked again eliminating JOLEN again. I notified ATC we were unable RNAV and requested a vector. When on the vector we agreed to try FMS 'both on 2' and flight director 'B.' The blanking stopped and I was able to re-enter the RNAV waypoints (it wouldn't take the departure since we were already on it). While re-entering the remainder of the waypoints; a Master Caution came on with the 'AFT DOOR' light. I called the Flight Attendant and asked him to check the handle. He pushed down on the handle and the light extinguished. As I returned to my pilot not flying duties finishing the departure data input and checking the rest of the route; I overlooked TEKBE. The oversight put us about 4 miles south of course when we were given direct SWB. We notified ATC of the error; and continued the flight without any further events.