As it turns out, there’s actually no way to prove that you don’t have malware on your machine. From a logical perspective, you can’t prove a negative.
You didn’t say what tools you’re running, so it’s hard for me to judge the answer to your question. If you’re concerned, let’s look at what you can do.
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Run a good anti-malware tool, like Microsoft Security Essentials. Make sure that both the program and the database are up-to-date so they can protect you from the latest threats.
Run Malwarebytes anti-malware. That’s a free tool from malwarebytes.org that’s very good at finding malware.
Consider running Windows Defender Offline if you don’t already run Microsoft Security Essentials. When you boot this program from a CD, software on your machine – in particular any malware that might be there – will not inhibit the ability of Windows Defender Offline to detect things. It’s also just a good idea to have a different program.
Of course, back up twice: before you do all of this and then after you think you’re clean.
Sluggish means malware?
Many people jump to the conclusion that a slow computer means malware. It could be, but other issues cause sluggishness as well.
I have a couple of articles – “Why is my machine slowing down?” and “How do I tell what program is slowing down my machine?” – which explain what’s happening with a pokey computer and what you can do about it.
It may be malware, but you definitely want to check all avenues before making the decision.