Sorry that is happening.
If it vibrates when you press the button, it would seem more likely a software issue. Newer Windows phones won't let a restore start unless the phone is well charged. So I would try restoring it again just in case the first restore didn't complete properly.
I didn't use Windows phones until Windows 8 but those and later have a hard reset option in the settings that returns the phone to as new. I think it restores a compressed image stored in the phone for that purpose so it does add to the cost of a device and may not be available. That might be a next thing to try if another restore doesn't fix it. Of course, you would have to then try your restore again or set the phone up all over.
I doubt the WDRT (Windows Device Recovery Tool) works on your phone due to the age BUT it's worth a try. Its a utility you can download from Microsoft to a PC that will reflash a phone with the most current version of Windows and microcode for that model phone. I did a quick check and couldn't find if your or other 7.5 phones are supported. May be worth trying it if all else fails. Like the Hard reset, the phone would be a clean slate afterwards.
Good luck.