DIAGNOSIS That's the sound of the water pump fighting an air lock or trying to pull water through a clog. Air gets trapped in the intake tube if the reservoir was empty or not seated properly.
FIX Turn the machine off. Remove the water reservoir, then firmly reseat it, making sure it clicks into place at the bottom. Add fresh water. This often primes the system and pushes the air bubble through. Turn it back on and try a brew.
IF THAT DIDN'T WORK The noise could be from a failing pump motor or a clogged intake filter (a small screen at the base of the reservoir inside the machine). If the pump is going out, the noise will get progressively worse and brewing will slow down.
HEADS UP That grinding noise is hard on the pump. If it happens frequently, it's a sign the pump is on its way out. Continuing to run it like that will lead to a complete failure where no water comes out at all.