Instead of configuring "any" (0.0.0.0 0.0.0.0), I would actually try the actual internal subnet for the dynamic statement.
It seems that the internal subnet is 10.10.10.0/24 base on the config, so you can modify the current dynamic NAT:
FROM:
object network obj_any
subnet 0.0.0.0 0.0.0.0
nat (inside,outside) dynamic interface
TO:
object network obj_10.10.10.0
subnet 10.10.10.0 255.255.255.0
nat (inside,outside) dynamic interface
And if you have multiple internal subnets, just configure the rest. And lastly, remember to "clear xlate" after the changes.
Also, if you are running 8.3.1, it might be a good idea to upgrade to the latest of 8.3.x. But if you are already running the latest, then it's fine.
If it still doesn't work, please run packet tracer on the ASA, and see where it's failing.