Hi, Cabcrusher, welcome to the forum.
Simple question, first off, what was the AV (of any) that you had installed before installing Avast?
Next, from what website did you get your Avast download?
And likewise, from where MBAM?
Please post the full addresses you went to to get these, the behaviour you are describing is not characteristic, in several ways.
Please right-click the "my computer" icon on your desktop, select "properties", and in the "general" tab (which it will open to) copy and post the information under the word "system", and also under the word "computer".
What is a NEMB?
Windows Defender is alive and well, and definitely still supported, you can get it
here, but don't bother, for now. Something is probably redirecting your searches or browser to a place you don't want to go, or preventing some legitimate connections being made.
This can be done, if not by me, then by some of the experts here.
Please click
here to directly download ATF cleaner. Save it to your desktop. The icon looks like a pale blue trashcan with the lid off. Double click it to run it. Place a tick in every checkbox, except history, and click on "empty selected".
This will not clean the malware, but it will make the cleanup easier, by removing all temporary files and reducing scan times; possibly taking some malware components at the same time.
Avast would not prevent you downloading Superantispyware. These two work together well.
Did you try updating MBAM before running a scan with it? If not, do that and try running a quick scan again.
There is no reason Asquared would have prevented you deleting what was found. (Incidentally, never delete anything found, when there is an option to quarantine it. Always quarantine, never delete.) So that is why I'm curious to know where you got your programs from.
What message was presented when you tried to remove these trojans using A2?
Spyware Blaster is not a removal tool, it's a tool to help prevent malware. Good to have, but won't help clean you up.
Last thing I want to know is the name, and a download link to the MajorGeeks removal tool you tried, please.
Don't worry.
Unless it's a particularly nasty file infector (possible) it should be removable, with a bit of methodical action.
If you have access to a clean computer, I'd be inclined to change any passwords to sites like ebay, and banks/credit cards. It may pay to inform your bank of this infection, and that you are taking steps to fix it, if you do online banking on this computer. Different banks have their own policies about customer responsibility in this area. I would think most would want to be informed.