So, if you power down your Exede modem your TV reception is better? With rabbit ears you are very susceptible to local interference. The router or computer itself may be a bigger source of interference. It costs $$$, but you might consider a satellite TV provider such as DirecTV or Dish.
Are you using actual "rabbit ear" antenna or are you using one Kent for HD TV? Reason I ask is I used to have antennas on each TV then went to bestbuy and bought a bigger like $99 antenna and have it in the Attic and feeds the whole house and for the most part works great. Actually get more stations then did with individual antennas