Ok, realized that hairlessupportmonkey was right... I needed a rule to allow ICMP on the DMZ interface. After adding the rule, still couldn't ping the interface. I could, however, ping from the DMZ interface to the attached core switch.
I then tried the Packet Tracer that stubnski suggested. Since I needed to choose a port, I used ssh and added a rule to allow ssh on the DMZ interface. Once it gets to the DMZ, it seems to fail with "Flow is denied by configured rule." Obviously I have something wrong with the access list config... I'll look at it closer and see what I can find.