Hi Estela,
Could you please apply captures on the outside interface and see if traffic is actually reaching the ASA?
I am just wondering(very unlikely) if the device connected on the outside of the ASA, is using icmp to determine if ASA is available.
Secondly if you do a packet-tracer command for one of the DMZ servers, it would clarify what the problem is:
packet-tracer input outside tcp 4.2.2.2 4222 det
Assuming, "outside" is the name of your outside interface, and the server you are testing connectivity to, provides a tcp service.
If any of the phases in the resulting output, show a "drop", that would point to where the issue is.
In case you need any help with the output, then please attach a sanitized config, and the output of the packet tracer command as well.
-Shrikant