Power button no longer turns screen on/off - apps don't fix this properly, cannot turn off phone to root it, help! I dropped my phone into water the other day and the power button has stopped working. What is odd though is that I can force restart the phone by holding power+volume down, it's just the power button on its own that doesn't seem to work.

I have tried various apps to remap the function to the power button but they are insufficient in one way or another (usually that it just stops working after a couple minutes of inactivity).

I have seen methods to remap the power button to the volume button directly, but this requires root access. Of course, this is a problem because I need to power down the phone completely (which I could do with the Tasker app), but I'm not sure if I will be able to turn it back on again after that.

Is there then a way to force the phone to boot into Download mode with the Tasker app? I can see that I can reboot with the types "Normal", "Recovery", "Bootloader" and "Shutdown". Is the "Bootloader" type just another name for Download mode?

Forgot to mention to phone - it's a Samsung A6
Most likely not. The bootloader should typically issue the standard reboot bootloader command. However, in case of Samsung, the command needs to specify the reboot download instead. An XDA thread mentions that the following adb command brings to the download mode - adb reboot download. Maybe you can use that instead?

As per this answer, Samsung phones do not support Fastboot mode. Most of the times you'd be living off ODIN, but can also use heimdall. Don't forget to follow its commands cheatsheet as it does seem to not support the standard fastboot commands. 

Also, I just wanted to remind you that if you are able to reboot the device with the Power + Volume Down combo, the same should also work when you shut down the phone but then fail to turn it back on.