Captain reports about B737-300 autothrottles (A/T) having trouble holding adequate thrust for cruise mach. Disconnected the autothrottles and noticed the #1 engine throttle would not manually move past the mid position (80% N1 at cruise).

Narrative

This aircraft came from the hangar; after an engine change (#1 engine). During cruise flight about half way to ZZZ1; we noticed the autothrottles having trouble attaining adequate thrust for cruise Mach. I disconnected the autothrottles and tried to manually set #1 engine throttle and found it would not move past mid position (80% N1 at cruise altitude). The throttle would come back; but still not go forward past mid. Called Maintenance Control and they thought it might be ice in cable. Power was controllable through an adequate range for normal operations; so we continued to ZZZ1 and landed without incident. Aircraft was taken out of service and repaired overnight in ZZZ1. Main Engine Control (MEC) cable box was not correct for that engine. We flew it to ZZZ2 the next day and seems OK now. Callback conversation with Reporter revealed the following information: Reporter stated he did not have any problem with moving the throttle back; but could not go forward past mid position. But on the ground; after they arrived; Maintenance started troubleshooting and noticed the same #1 engine throttle was also binding when moving the throttle aft to idle. Reporter stated he was told the Main Engine Control box was not correct for the #1 engine that was replaced the night before.