MacBook Pro boots to mostly white screen with random pixel pattern
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:


Power off your MacBook Pro.
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.
Hold those keys down until your Mac reboots again (i.e. a 2nd time) and you've heard the startup chime twice.
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:


Power off your MacBook Pro 
Power on your MacBook Pro
Press and hold the D key before the gray startup screen appears.
After a while, Apple Hardware Test (AHT) will start.
When prompted, select your language and click the right arrow. 
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.
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.