Hi Jeremy,
There can be a number of things, firstly I'd say check the following
1) Are you running nat-control (sh run nat-control)
2) Do you have any nats setup ( sh run nat, sh run global, sh run static)
3) Check your inside access-list if defined, if not ensure your inside security level is higher than your outside security level.
4) finaly try a packet-trace which should give you some cryptic output, but will help...
packet-trace input inside icmp 192.168.1.16 8 0 4.2.2.2
(this will do a echo (type 8 code 0) request from interface named "inside" 192.168.1.16 to 4.2.2.2 and shows if its allowed or will be dropped, if the above doesnt help, post the output of this into the errr...post!
Cheers,
Rich