When your computer is acting weirdly and you can't find any reason for the behaviour, that age old advice to turn it off and on again really is the first thing you should try. However, that may not solve your issue, and so we’re going to look at a few other techniques for tracking down problems that may or may not represent malware activity.
Get a second opinion
Antivirus programs aren't perfect. Sometimes it takes them a while to recognise a brand new threat. If you really think your system has been infected, get a second opinion from another antivirus tool. Try one of the clean-up-only free antivirus programs, to start with. By using a clean-up-only tool you'll avoid the possible conflict that can occur when multiple real-time antivirus engines are running at the same time.
You could also try a free online scanner. Trend Micro's HouseCall is a well-known example; Bitdefender also offers a free online scan. Many security vendors offer something similar. If the online scan finds a threat, you can work with your antivirus software’s tech support to get it fixed.
Check browser add-ons
Sometimes it seems the difficulty is specific to the browser. Pages don't load properly, or browsing is super-slow. Browser problems might be caused by a flawed add-on, either a tool you installed yourself or something installed by a drive-by download. To check this possibility, launch the browser with no add-ons running (see here for guidance with Internet Explorer, here for Chrome, and this page for Firefox).
If launching the browser with no add-ons eliminates the problem you've experienced, clearly one of the add-ons was the cause. Close the browser, restart it normally, and experiment with disabling add-ons one by one until you find the culprit.
Check startup programs
Most malicious applications don't just run and quit; they need to launch again when Windows reboots. Plenty of valid programs launch at startup too. If one of them is defective it could be the source of your troubles. Using MSCONFIG, the System Configuration utility, you can check whether a startup program is giving you grief.
Click the Start button, enter MSCONFIG, and then click the tab labelled Startup (in Windows 8, this will direct you to click through to the Task Manager). This tab lists all the programs that launch at startup, with a checkbox indicating which items are enabled. (With Windows 8, there’s simply a Disable button). To begin with, un-check all the boxes or click the Disable all button. Click okay and reboot the system.
Is the problem gone when Windows finishes rebooting? If so, one of the startup items was the cause, so it's time for some slightly tedious sleuthing. Launch MSCONFIG again, re-enable just one startup item, click okay, and reboot. Repeat until the problem rears its ugly head; then you've found the problem startup item. Of course, if disabling all the startup items didn't help, you'll want to re-enable them.
Try Safe Mode
If your system problems are so severe that you can't even launch MSCONFIG, it's time to try Safe Mode. Turn the computer off, restart it, and then start tapping the F8 key about once per second. After a bit you should see an all-text menu. Select Safe Mode with Networking from the menu and press Enter.
In Safe Mode, Windows loads a bare minimum of drivers. Programs that normally launch at startup don't launch. Because it uses a lowest-common-denominator video driver the display is pretty ugly. Still, Safe Mode often lets you work with the computer despite problems that cripple normal Windows.
Try disabling all startup items with MSCONFIG, as described earlier. If the problem is gone when you reboot back to normal Windows, it means a startup item was the source of the trouble. You already know what to do about that.
There's a limit
With the PC running in Safe Mode there are other avenues to explore, but you're right on the edge of what amateur troubleshooting can accomplish. You can try checking system settings, and perhaps undo any recent changes. You can scour the Internet for possible solutions. But if in the end you must resort to a hired technician (or a clever relative), at least you'll be able to offer an impressive list of possible fixes you've already attempted.