I've seen AVG cause problems before and while I'm not saying it is responsible in this case, either turning it off or using its Uninstaller to eliminate it would be a first step I would take.
I use Norton Security on two laptops and it has blocked an otherwise known safe program on one machine while not taking any action against it on the other.
You can force a Safe Mode boot through msconfig by going Start - type msconfig and press enter then under the Boot tab check the box for Safe boot and then the one for Network - Apply - Ok then reboot, but do not check the box to make settings permanent.
You can also use the bcdedit commands from a command prompt run as an administrator to boot into the various Safe boot options, but Group Policy in Home Premium is a difficult one.
http://www.sevenforums.com/tutorials/69585-safe-mode.htmlThe reason for running Windows Repair in Safe Mode is to isolate the AV program as it can interfere with the Permissions and you don't need the Networking aspect of Safe Mode for Win 7, so see if any of the alternate options to boot into Safe Mode will work and then run WR a couple of times.
If disabling or uninstalling AVG or any of the alternate methods don't resolve the Safe boot problem, then disable AVG and then run WR.
Windows Firewall will still be active but you could disconnect from the Internet for the duration.
As you suspect, a boot sector infection will also prevent you from booting up into Safe Mode and a scan with the Kaspersky Rescue disk is recommended to check for that.
This article recommends running Combofix but I think it is a dangerous program in that it can take out legit files - it did once for me, so create an external system image before running it.
https://malwaretips.com/blogs/cant-boot-into-safe-mode/