Air taxi First Officer reported having communication problems with ANC Ground Control that may be due to interference from construction causing a radio dead zone on the ramp area.

Narrative

This morning after engine start at the Anchorage Ramp I overheard another company aircraft experiencing trouble contacting Ground Control on 121.9. We (myself and the Captain) could both hear our company and the Ground Controller clearly but it appeared that Ground could not hear company. They eventually contacted Clearance Delivery for taxi instructions. Approximately 1 - 2 minutes later I tried contacting Ground on 121.9 three times; at about 1-minute intervals with no response. At this point I tuned 121.9 in our secondary radio and was successful contacting Ground and received taxi instructions to hold short [Runway] 33 at [Taxiway] S. I tuned Tower in my number 2 radio and received instructions to cross 33 at S; continue Y K HS at S. On the taxi; the Captain retuned my radios to normal setup; tuning Tower in the radio 1 and our company frequency in number 2. He did not reselect my audio panel so my transmissions were now on company instead of Tower frequency. I did not catch this. Tower cleared us for takeoff which I unknowingly acknowledged on company rather than Tower frequency. Tower then handed us off to Departure; while making the frequency change to Departure Control I caught the mistake and selected the correct radio for comms with Departure.Discussing the event later with a crew from a third company airplane that was on Ground frequency at the time; they could hear both us and the previous crew from the east side of the airfield on the far side of the Control Tower. They did not hear me read back Tower's instructions but commented that we must have heard Tower because we turned our lights on and departed.There were two items together that combined set me up for this mistake. The first is a potential problem with ATC radio equipment on 121.9; possibly interference from construction; creating a dead zone on the ramp just as Taxiway Sierra enters the north ramp. The second factor was a CRM deficiency between myself and the Captain where one pilot changed equipment on the other's panel without communicating what was changed.