You probably have a faulty piece of hardware, from my experience likely your HD. If you are connect to a network share (SMB) and having connectivity issues that also could cause hangs. The drag and drop slowness in general points to the "explorer" process hanging, the same process used to communicate with network resources (file shares for example).
This is most likely not faulty hardware.
On Windows, there are occasional messages that are broadcast system-wide to all top-level windows. If a window does not respond (or is slow in responding), then the whole system will appear to freeze. There is a built-in timeout and if exceeded, the system will assume that the window isn't going to respond and it skips the window (this could be the 10-20 second delay you're seeing although I think the timeout is a little higher than this).
I have not seen a solution for tracking these kinds of problems. You might experiment by creating a program that sends individual messages to each top-level window and record the time taken for each to respond. This isn't failsafe but it's a starting point, and this is (if I recall correctly) the technique I used to identify such a problem with Adobe's iFilter (for the Microsoft indexing service).
But before you go down this path, you said that these are recent problems. See if you can figure out what you might have installed recently and then uninstall it. This includes Windows patches as well as any new drivers or applications.
Are you able to peg it to a rough time-frame of when the symptoms started? If so, you could match the critical updates/installs in Add/Remove programs to that estimation and start looking there.
More generally, I find using MSCONFIG to temporarily turn off all startup programs and all non-Microsoft services can help quickly divide and conquer - If the symptoms disappear, you have a shorter list to work through.
Safe mode (with or without network - see next idea) is another way of narrowing the list of suspects.
Since it is multiple machines, if it were hardware it would have to be something common... Especially if it is two different locations. That said, network connectivity (or lack thereof) is the other frequent culprit. Bringing up a system in a standalone config (net cable unplugged/wireless radio disabled) will seem VERY slow at first, then once the timeouts and various retries have been exceeded, should zip along, especially if you are still running in a limited startup environment. I have had recalcitrant switches/routers be a problem, as well as sluggish external services (like an ISP's DNS) cause symptoms like this.
No floppy, optical, or other removable drive access at those times?
To diagnose the activities or infiltration a rootkit or other malware uses, you might check out the forums on Bleeping Computer, some of the volunteers there who help people remove such may be willing to help you figure out where to look for such infestations.
I recently cleaned up some malware through the help of an expert on that site which I also needed to use a third-party tool (in my case Malwarebytes) to remove, but the malware was relatively new such that this tool couldn't fully clean out the stuff until a more recent update to its definitions got released.
I still don't know how or where exactly to look on a given system for such an infestation, but that site might hook you up with someone who has that expertise. As long as you emphasize that you're looking for this to be able to track down such and not for purposes of writing your own malware I would hope they'd be receptive to your request.