Constant restart mode

Was it a time machine back up??? If so they are not bootable you need to restore the data to a new drive in the machine. Or use a cloned copy of the original bootable disk.

You also give no idea which model you are using if it’s a 13 inch 2009 -2012 it’s possible the flaky SATA cable has died an easy and cheap replacement.

 

OP wrote:
"I have a 2011 MacBook Pro 15”"

Very strong possibility that you have just encountered "RadeonGate".
If you don't know what that is, better research up on it.

In brief, the 2011 MacBook Pro 15" and 17" models had a discrete GPU that over time has a very high probability of going bad on you.

Apple -had- a motherboard replacement program, but that's ended and I don't think they'll even work on these older machines any more.

You could replace the motherboard, but the replacement will also have a high likelihood of failure.

Honestly, not worth putting any more money into it. This particular model was one of "Apple's worst clunkers", insofar as reliability is concerned.

Time to shop for something new or refurbished.

You can take the hard drive OUT OF it (very easy procedure), put it into a USB3 enclosure (or use a USB3/SATA dock or USB3/SATA "dongle adapter"), and get your data from it, and then keep using the old drive for extra storage.

A good replacement worth considering is the 2015-design MacBook Pro 15".
These are still available from Apple as "new builds" (you have to go to the 15" MBPro page on Apple's site and click the buy button, then scroll down to see them). They're also available as Apple factory-refurbished.
From reports posted here, the 2016-17 MacBook Pro's are having too many problems (particularly with the keyboard) to consider...