It's probably an issue with wireless signal interference.
Microwave ovens and most common wifi transmitters share the same frequency band(2.4 GHz).
Changing to a newer router wouldn't help either as chrome cast, as far as I know, only supports 2.4 GHz.
My suggestions for fixes are:
- Changing what channel your wifi setup is on.
- Moving the microwave oven.
- moving the wifi router.
- buying a more isolated microwave.
- using direct connection from the computer to your router (as the chrome cast is still connected this probably won't help).
- accepting defeat and buy pre-popped popcorn for the next movie night ;-)