Don't know where you got mbam_rules.exe, that doesn't appear to be a current file. The manual update file can be found Here
http://malwarebytes.gt500.org/
But for the moment see if you can do the following without the manual update.
Also, for the moment, only try using either IE or Firefox since both are all ready on the computer.
Try booting the computer to Safe Mode with networking. Not sure what operating system is on there but try going this way.
Turn the computer on and tap the F8 key until you get the choice screen and choose Safe Mode with networking. This should get you online but in Safe Mode.
Then see if you can update MBA-M. If you can do a Full Scan in Safe mode, have it Remove everything found and Reboot. This is a must as some of the removals must be done early in the boot process.
Using IE see if you can get online. Don't install AdAware, it will do nothing.
Run another full scan with MBA-M and again have it remove everything it finds and reboot again.
Then try and see if you can Download DDS by sUBs and save it to your Desktop.
Be sure follow the instructions below carefully!
• If your AV has a script blocker, please disable it
• DoubleClick on dds.scr to run the tool
* A command box will open, displaying added information for your reading pleasure while DDS completes its scan.
* Upon completion, a Dialog Box should open instructing you to save and post the TWO resulting logs (DDS.txt & Attach.txt).
• Copy&Paste both the DDS.txt and the DDS Attach.txt into your reply, along with the logs from MBA-M.