To follow up: I've scanned with Norton AntiVirus and with Malware Bytes. No problems were detected.
After rebooting, I tried launching Firefox (safe mode). It took a long time to open, just as the regular Firefox did.
Again, this only happens when first booting up. Afterward, browsers work fine, and I'm not noticing any problems with speed or anything else. While waiting for the browser to launch, I checked Task Manager, but didn't see anything unusual going on. I hear the disc running, but the system resources are in the single-digits, nowhere near 100% usage.
So, I'm still puzzled. Anything else that I should check?