Voltage on a digital multimeter looks like an open circuit to the circuitry you are trying to measure. Therefore, it can't hurt the measure while the circuitry is "hot" as long as you are in the correct setting.
If, however, you inserted the leads with the circuitry on, but the multi meter off, you ran the very real risk of a short circuit when turning your meter on.
it looks like the OP made the simple but easy to make mistake of shorting the circuit by having the multimeter on the wrong setting. Either Ohms, or current, and not voltage.
I can't think of one Engineer or Technician that I know, including myself that has no fried a circuit by not paying attention to the setting on the multimeter.
I would open the amp (unplug it first) and do a very close inspection of the circuit boards to see if there are burned traces or components. Look closely.
Something was going bad and fried, or partially fried.
take a look.
enjoy