Part 91 Pilot reported while entering the DMW traffic pattern had a NMAC with another aircraft 300 feet below and passing behind them.

Narrative

Approaching Carroll County airport (DMW) from the West on a northerly track at 2;100 ft. MSL; I noted on the TIS That there was multiple incoming traffic from the northeast inbound towards DMW; including one aircraft that was calling 7 miles out to the northwest inbound on an instrument approach. From my position it looked like I could have entered the traffic pattern from a high crosswind from Runway 34 at approximately 2000 feet and get ahead of the incoming traffic. I was West of the airport approximately a mile and a half to perhaps 2 miles from the airport and in evaluating the number of traffic that was inbound to the airport I decided to enter the airport pattern from a high extended crosswind from Runway 34. I heard an aircraft call out that it was taking the Runway for departure from 34 and myself and my crew were looking for the aircraft. At about this time; the MFD in my aircraft suddenly failed and had basically become frozen and inoperable. There was now no TIS information being displayed. I pulled the breaker on the MFD and reset the device and continued on with the approach. Upon reaching near the extended center line of Runway 34; I suddenly saw an aircraft approximately 300 feet below my altitude off my 1 to 2 o'clock position flying towards my tail. The aircraft was approximately 300 feet below my altitude and would quickly pass behind me so no evasive action was taken. I was flying above the traffic pattern altitude at 2;000 feet so I had believed at the time I was at a safe altitude for any departing traffic which would normally climb out to 1;300 feet before making any altitude or heading changes. I was able to reset my MFD but when it came back alive it was still not functioning properly. I continued to the airport and entered a downwind pattern; but because of other incoming traffic entering the downwind; I elected to simply climb in the pattern and remove myself from the pattern to the South and then come back and join the approach to downwind from a 45° angle and landed without incident.