MacBook Pro turns on with a pinkish screen

It sounds like the display has failed or there is a problem with the GPU on the motherboard. Although your model can restore the same OS that was installed in Recovery Mode, it cannot do an Internet Recovery. If there is a version of OS X from 10.7.x and later, then you can reinstall it in Recovery Mode.

Install El Capitan or Later from Scratch

If possible, back up your files.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the target drive (out-dented entry w/type and size info) from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the partition scheme to GUID.
6. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
7. Click on the Apply button, then wait for the Done button to activate and click on it.
8. Quit Disk Utility and return to the Utility Menu.
9. Select Install OS X and click on the Continue button.

An Internet connection is required and the Recovery HD partition must be intact. Otherwise, you will need the two Software Restore DVDs that came with the computer from the factory. Boot the computer from Disk 1 in order to install OS X 10.5.x.

If you have a copy of the retail Snow Leopard DVD, then you can use that to install Snow Leopard 10.6.3. Or, you can get Lion 10.7.5 from the online Apple Store. You can purchase Lion at the Online Apple Store. The cost is $19.99 (as it was before) plus tax.  It's a download. You will get an email containing a redemption code that you then use at the Mac App Store to download Lion. Save a copy of that installer to your Downloads folder because the installer deletes itself at the end of the installation.

Sounds like you're facing a GPU malfunction. The cost of repairing your Mac may exceed its value, so the only feasible option is to consider upgrading.

You can't, if that is what happens. The problem may require hardware repair.

What are you trying to tell me? The procedure I posted doesn't require you to download anything to the computer beforehand. The installation is done from an Apple server, remotely.

Of course, if the computer won't start, then there is nothing you can do but get it repaired.

If the Recovery HD is still working, then try the procedure I posted earlier. That will attempt to reinstall Sierra after erasing the target volume, usually labeled "Macintosh HD." Here is the little change needed:

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the target volume (indented entry, usually, "Macintosh HD") from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the partition scheme to GUID.
6. Set the Format type to Mac OS Extended (Journaled.)
7. Click on the Apply button, then wait for the Done button to activate and click on it.
8. Quit Disk Utility and return to the Utility Menu.
9. Select Install OS X and click on the Continue button.

If it's an Early-2011 model, then see Computers that can be upgraded to use OS X Internet Recovery. If it's a later model, then you can use Internet Recovery:

Internet/Network Recovery of El Capitan or Later on a Clean Disk

   If possible, back up your files before proceeding.

1. Restart the computer.
2. Immediately, at or before the chime, hold down the Command-Option-R keys until a globe appears.
3. The Utility Menu will appear in from 5-20 minutes. Be patient.
4. Select Disk Utility and click on the Continue button.
5. When Disk Utility loads select the target drive (out-dented entry w/type and size) from the side list.
6. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
7. Set the partition scheme to GUID.
8. Set the Format type to APFS (SSDs, only if installing Mojave or Catalina ) or Mac OS Extended, (Journaled.)
9. Provide a volume name, usually "Macintosh HD."
10. Click on the Apply button, then click on the Done button when it activates.
11. Quit Disk Utility and return to the Utility Menu.
12. Select Install OS X and click on the Continue button.