MacOS – Mbp early 2011 stuck at white screen

Here is what you know from your excellent details:

1. The keyboard isn't working since all of the shortcuts get handled from the firmware in the Mac.
2. The Mac can't find any bootable OS X due to corruption or hardware failure

Why the keyboard isn't working isn't yet clear. I would disconnect everything including the power and then remove both RAM sticks - noting which was on the top and which was on the bottom.

Next, plug the Mac in and power it up with nothing connected. You should get three beeps indicating the POST (power on self test) detected no RAM. If you have severe hardware problems, it won't know the RAM is missing and you'll know you need to get inside to fix it.

Assuming this works, power it off after waiting to see if it boots in 5 minutes time (really wait that long for the Apple logo to show up). While you are waiting listen carefully for rhythmic noised from the hard drive. It shouldn't keep seeking past the first 45 seconds and if so - you will know the controller or the drive is faulty. It should spin quietly after a few minutes or be reading the drive if it's corrupt and the hardware / OS is trying to fix things.

Next - power it off by the button and put the "top" piece of RAM in the "bottom" slot and repeat. Lastly - if you get to the white screen at this point, try another keyboard (command-s or shift held down are the best options here for troubleshooting) to see if you can isolate the failure further.

I tried to make some assumptions about what is wrong and you can edit the question or ask another with the step that fails referring to this question if you want to isolate things further before attempting a repair.

The A1286 is the model number used for many of the 15" MacBook Pros from late-2008 to mid-2012.

Troubleshooting is a process of elimination and often requires patience. In this case you should definitely run Apple Hardware Test, although you could try resetting the NVRAM first to see if that resolves the issue. Below are steps on how to do both.

Resetting the PRAM/NVRAM on your MacBook Pro model

Older Macs had what's called Parameter RAM (PRAM), newer Macs use Non-Volatile Random-Access Memory (NVRAM). It may be worth resetting this on the off chance it resolves your issue. Here’s how to do this:

1. Power off your MacBook Pro.
2. Press the power button and then press the commandoptionpr keys. You have to make sure you press these keys before the gray screen appears or it won’t work.
3. Hold those keys down until your Mac reboots again (i.e. a 2nd time) and you've heard the startup chime twice.
4. Let go of the keys and let your Mac reboot normally.

If this doesn't work, then proceed to testing your hardware with Apple Hardware Test.

Run Apple Hardware Test

Your model MBP uses Apple Hardware Test. To use this, follow these steps:

1. Power off your MacBook Pro
2. Power on your MacBook Pro
3. Press and hold the D key before the gray startup screen appears.
4. After a while, Apple Hardware Test (AHT) will start.
5. When prompted, select your language and click the right arrow.
6. When the AHT console appears, you can choose to run Basic tests by clicking the Test button. However, I suggest you select the "Perform extended testing" checkbox before you click the Test button.
7. Your test results will appear in the window in the bottom-right of the console.

Note 1: that the extended test will take some time. Take a note of the results and report back.

Note 2: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete.