dont repair or reinstall, read this:
Since i dont have new ideas why minidump cant be stored so let's summarize what we know:
- problems were came out when you installed avast
- the crash on shutdown may be caused by aswTdi.sys driver (e.g. conflicts between network drivers)
Try to rename aswTdi.sys, reboot and shutdown - is there a BSOD ?
a) if yes, rename aswMon.sys and aswMon2.sys - reboot and then shutdown - BSOD ?
b) if not, copy & paste here all *.sys drivers from your <windows>\system32\drivers - there must be a driver which doesnt work well with aswTdi.sys