Ongoing USB(?) Problem

I've been having some longstanding problems with my keyboard that I'm beginning to think represent a broader problem with USB on my iMac.

I have a late-2009 model 27" iMac, running El Capitan.

For the last year or more, I've had a sporadic problem in which, when I turned the computer on, it does not recognize my wired Apple keyboard. In order to get it to do so, I have to reset the SMC and NVRAM. Sometimes it's hard to do the latter because it won't recognize the keyboard so that I can press Cmd-Opt-P-R. But usually after a couple of tries it works and then all is fine (and I try not to turn my computer off so that I don't have to go through it again).

I've tried purchasing a new Apple keyboard, but it didn't make the problem go away.

Today I attempted to boot in Safe Mode, which was a challenge, as holding Shift didn't do anything the first few times, because the computer stopped recognizing the keyboard again. I had to use the mouse + the keyboard viewer to go to Terminal and force it to boot up in Safe Mode (which also took 3 tries: the first time it powered off partway through, the second time it booted to a cursor and blank grey screen, and the third time it made it to a login prompt). Once in safe mode it still wasn't recognizing my keyboard. But the next reset (plus another SMB/NVRAM clearance) it finally came aboard and booted successfully in safe mode plus my keyboard was recognized.

So, an ongoing problem. In the meanwhile, I've lately bought an iPod (6th generation Nano), and its behavior suggests to me that I may have a broader USB problem, of which the keyboard is a symptom.

The iPod works just fine on a friend's MacBook (not sure the model, but can track this down if it becomes relevant). However, when I connect to any of the 4 ports on my iMac, the iPod will not mount as a drive. The system does, however, recognize that something is plugged in. Under System Information, it shows up under USB 2.0 Bus --> Hub --> iPod. So, the iMac is aware there's an iPod plugged in, but won't mount it or let iTunes talk to it.

The iPod will show up as a mounted drive when I plug it into the one of the keyboard USB slots (but only one specific one, on the right, not the other). But iTunes hangs up any time it tries to communicate with the iPod, such as when trying to restore it, or when trying to transfer files. Occasionally one song gets synced, but generally it just stops working and says that "iTunes could not copy X to the iPod Y because the file could not be read or written." iTunes is up to date.

I posted initially under the iPod forum about those problems, but I'm thinking now that this, plus the keyboard issue, is symptomatic of a larger issue with my iMac and its USB ports, and perhaps someone here can help me pin it down. Thanks!