I'm curious to know what were your first thoughts and actions in this situation.
Seeing IAS, ALT and AOA disagree messages on the 737NG might suggest an ADIRU problem (in the absence of probe heat failure indications or birdstrikes). A deeper knowledge of 737NG systems would be required for "A/T LIM" diagnosis.
I'm wondering if drip tray design has improved in the last few years. Their failure has been known to cause multiple computer failures with serious consequences.