Super King Air 350
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 45; Flight Crew Total 11500; Flight Crew Type 350
Confusion; Distraction; Situational Awareness
Deviation / Discrepancy - Procedural Clearance; Ground Incursion Runway; Ground Incursion Taxiway
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented
Chart Or Publication; Airport; Human Factors
We were cleared to taxi to Runway 28 via E; cross 35/17. We had moving map of taxiway on the MFD and as we approached E1 the map showed a bend to right. We followed the map more than paying attention to signs and turned onto Taxiway E1. The Tower stopped us; then cleared us to taxi on Runway 4/22 to Runway 28. We should not have concentrated on the MFD map as closely as we did.  We should only have used it as confirmation of taxi signs.  Note: Earlier Runway 4/22 was closed.  I don't know if it was still closed when we entered taxiway E1; if we went onto Runway 4/22 or if Tower stopped us prior to doing so. The surface markings were faded and we could not tell if we were on Runway 35; Runway 4 or just E1.
Cleared to cross Runway 17/35 and taxi to Runway 28 via Echo at WAL; the flight crew of a Super King Air inadvertently entered E1 enroute and may have incurred on Runway 4/22. Ground Control alerted them and provided an alternative clearance to Runway 28. Over-reliance on a moving map airport MFD display likely contributed to their error.