It sure sounds like a power problem. Since your system was working well with the components (wire/connectors) you have, logic would suggest that the change is related to one of two things: 1) ground connections or 2) positive power supply.
Generally the amp "on" signal is very low power and wouldn't be affected by the voltage drop when you apply the brakes or turn on the lights, etc.
You should check everything for a good solid mechanical connection; good electrical connections --at the battery, fuse, distribution block(s). Feel for any unusual heat in these devices... a marginal connection will often heat up a bad connection (but not always.)
The ground to the amp(s) should be the same gauge as the power cable.