I sent my damaged P4P to DJI on Monday, April 10th, and haven't heard anything at all back from them.
I packaged it using the mailing label they sent me and sent it via UPS (go Brown). How long does it take for
DJI to at least acknowledge they've received it?

It takes several business days to check in and update the system, I'll keep an eye on its process  for you, no worries.

First, with their prepaid shipping is very slow so keep track of when it arrives in Cali. Second, it will take at least a week after they received your drone to open it since they are back logged so bad, I'm going threw the same process and was told 10day turn around time..going on 21 and they just opened it today

With DJI care it isn't as long of a wait - still took three weeks time, but if they have received your package and checked it in, it should be a matter of about a week for the work to be completed. I am speaking from experience, I sent mine out on the 14th of March and got it back on the 7th of April.

Mobilcams Posted at 2017-4-19 17:45
With DJI care it isn't as long of a wait - still took three weeks time, but if they have received your package and checked it in, it should be a matter of about a week for the work to be completed. I am speaking from experience, I sent mine out on the 14th of March and got it back on the 7th of April.

Mine is DJI Care, they gave me the back logged story over and over.,,oh then they moved locations bull