Why isn’t my Mac restarting

"Why isn’t my Mac restarting: why does my Mac have a problem signing into my network after erasing my mac"

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So, what's the problem?

You're asking two questions here in one thread. There's lots of ways to troubleshoot the power. Here are just few to try (depends on the model).

Will it not connect? Does the connection go away? Does it not show? Are you trying to format the disk, but cannot connect? You might need to install firmware updates (which requires an install of its own). So, if you are at the Recovery Screen, then add it manually(top-right corner). If not connecting, then forget the network, and then add it back. Restart the Mac, as well.

Use Ethernet: The ultimate solution here, to me, would seem to be to use Ethernet to get the macOS installed:

Belkin USB-C to 2.5Gb Ethernet Adapter - Apple

Revealing the Mac Model and Year:

Obtain the Serial Number:

1. Go to: Utilities menu
2. Select: Terminal
3. Use this Command:

ioreg -l | grep IOPlatformSerialNumber

then...

Enter the serial number here: https://checkcoverage.apple.com