Macbook Pro freezes and shuts down.

Sounds like a GPU issue

to rule out your Display you can plug in an external monitor and see if all is well.

If you see the issue on the external display it confirms the GPU.

see vintage and obsolete:

Obtaining service for your Apple product after an expired warranty - Apple Support

Obtaining service for your Apple product after an expired ...

while it is entirely possible, there are no reports of dark screens caused by GPU issues.

What happens far, far, more often is that users have added software that interferes with macOS.

Consider downloading and running this little "discovery" utility, Etrecheck. It changes NOTHING. Etrecheck was developed by a senior contributor here, and uses mostly system calls and simple tests to collect often-needed information.

it contains little tests for speeds of devices, CPU utilization, memory usage, energy usage and a digest of recent problems, in one easy to use package. it does not even need to be Installed. Because less can be learned when your Mac is running great, best time to run is when your problems are actually occurring, if possible.

if you follow the directions faithfully, its report (pre-laundered of all personally-identifiable information) can be "Shared" to the System ClipBoard, then Pasted into an ‘Additional Text’ window in a reply on the forums.

Use Etrecheck Pro for free:

http://Etrecheck.com

The amount of data you get can be daunting. If you POST your report, some Readers here are willing to look over those reports, and can provide valuable insights.

Then start reply on the forums, click the "additional text" icon, and PASTE

When your computer can not power on, it often can not charge the battery in the usual way either. But it can often trickle-charge.

Connect the power adapter and leave it connected, at least overnight.