it sounds like you are missing the event answered or network reached message (sorry can't remember the exact message but it is something along these lines) in NICE. Check you have installed the correct Cisco client in NICE and configured NICE to the correct version of Cisco. Also what integration are you using? TAPI, JTAPI, CG or CTIOS, I have had issues with CTIOS previously and had to revert to CG as a quick fix at the time.
Some days I do my job, other days it feels like I'm doing everyone elses job, other days I should have stayed at home and mowed the lawns.