possibilities

Possibly your house electric is wired wrong and turning the light on is drawing too much power for the circuit you have it on for either the TV or the converter and that change is causing the issue, or your house wiring is causing electrical noise and is being picked up by either the HDMI or ethernet cable. Both cases require a electrician to verify your electrical set up, the later may also be beneficial to replace the HDMI and ethernet cable but the electric should be looked at for safety issues. ti can be a loose neutral, floating neutral, loose hot, bad ground, etc. causing the issues.

In the case of overdraw you can run an extension cord from a different outlet not on the same circuit [ie keeps power when you turn the breaker off for the TV/hdmi converter] though if something is massively wrong with the power, like you live in an old apartment not intended on housing this amount of wattage using devices, there is not much you can do but get a power regulator or beg the landlord.