Small Transport
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 5.5
Confusion; Distraction; Situational Awareness
ATC Issue All Types; Airspace Violation All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance; Flight Crew Returned To Clearance
Human Factors; Procedure
I received a position relief briefing that Aircraft X was non radar at 8;000 feet and was going to report the Denver Approach boundary.  I was also briefed on two aircraft deviating for weather that were in conflict with each other.  The first thing I did after taking the sector was to turn the traffic conflict.  It was a shallow convergence and required two turns totaling 30 degrees and constant monitoring. I also had some other coordination to do for an aircraft that was wrong for direction.  I couldn't remember if the previous controller had mentioned it in the briefing or whether or not it had been coordinated so it added to my workload.  At some point during this time Aircraft X's data block began flashing an MSAW (Minimum Safe Altitude Warning) alert.  He was heading into an area with a higher Minimum IFR Altitude (MIA) of 9;000 feet.  For some reason I dismissed the alert.  I had previously been aware of the higher MIA but it didn't click pertaining to this aircraft. Even though I saw the words MSAW I think I instead assumed that the data block was flashing in coast track because he was still non-radar.  The alert flashed for a long time before I finally realized what was going on. I climbed him to 9;000 feet and as he came back in radar he was in the higher MIA area still climbing out of 8;500 feet.I can't think of any recommendations.
A Denver Center (ZDV) Controller reports of an IFR aircraft that was non radar at the time and was expecting it. Minutes later the data block started flashing on the aircraft indicating a MSAW. The controller dismissed the alert before realizing what was going on. Eventually; the controller climbs the aircraft to a safe altitude.