Uninstall Avira completely using the programs own uninstaller if available or the Programs and Features applet in the control panel. You may want to follow that up if need be with a removal tool specific for that product either from the vendor or from the listed provided here
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Replace it immediately with MSE from here
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It looks like it may have let you down if this driver is what I suspect it is
a5f1wq9m.SYS 12/27/2011 nothing out there on the vast information super highway regarding that file and that makes me suspicious.
You may also want to consider running an off line scanner such as this one found here
What is Windows Defender Offline? (get the correct version for your system architecture) it will create a bootable CD for you to start your computer from and run a
FULL system scan (defaults to Quick Scan, change that) independent of the operating system.
Regards and keep us posted
Randy
P.S. Interestingly none of your .dmp files after 07-09-2012 would open in WinDbg and pitched an error. So any new dump files after completing the above might help further the diagnostic process.
If Blue Screens persist then start here;
And get rid of this driver
sptd.sys 3/3/2012 Usually associated with Daemon Tools or one of the Alcohol products. Use this program from here (again get the correct version for your architecture)
Link Removed download and run it and be sure to click the UNINSTALL button.