Sounds like a DSP problem to me. Normally inbound calls start at PRI channel 1 and work up while outbound calls start at 23 and work down. Since your problem is outbound the DSPs associated with the PRI high channels may be faulty.
These are the paths to get to each CCX logs through CLI. They may be helpful if you are having issues accessing RTMT or downloading logs through it.
If you want to download them you have to prefix "file get " and you can add one of the options (re...