This is a fun question.
For me it was the mid-80s. Back then, there was no Windows, and there was no Web.
At that time you could dial in (literally dial, using an acoustic coupler modem, the kind where you put the handset in the cradle) to Telenet or TYMNET, and get access to the internet through some host you had access to. Dow Jones News Retrieval and Compuserve were also portals in those days.
Since there was no web, a lot of the connections between hosts were intermittent, provided by UUCP. You could access Usenet (remember newsgroups?) and then there were BBS (Bulletin Board Systems) some of which were UUCP enabled and some were not. FTP sites were the main way to access data, aside from Usenet.
The first web servers didn't come until years later. In the early days of "the web" things weren't even graphical. You could use programs like Lynx for HTTP access, or there was also Gopher. IBM used to operate a great Gopher server. HP had one of the first really useful web sites. No marketing crap, all just useful info.
You guys better not get smart about those floppy drives. I used to have a job aligning those with an oscilloscope. You didn't throw away a floppy drive then as it cost about $400.
Rod, your coprocessor would have been the 8087, and it would have been paired with the 8086. The 8088 didn't have a math coprocessor, as I recall. But your work really splashed out, going for the 360k drives. Those were the double density ones!
Those were the waning days of CP/M. I was doing a lot of CP/M programming back then, for 8080 and Z80. DOS was beginning to achieve popularity.
I remember back then seeing an ad in Byte when someone came out with a 1-Megabyte memory chip, which at that time was a f-ing lot! A thousand dollars it cost. A thousand dollars a meg for memory. You didn't even have 10-baseT networking then, we were all using coax.
By the time Windows 3 came out I was mostly doing Unix admin. Desqview/X came out around the same time, and that seemed cooler to us, because it integrated better with the unix machines. It was a real pain back then getting Windows to network properly. There was no built in TCP/IP support, so you would have to load DOS-based networking stacks, either from Novell or KA9Q or later Clarkson. And by that point there was the twisted pair 10baseT ethernet standard, so networking because easier...
Things were more fun then it seemed. The internet was more like the wild west, and there weren't many idiots on it. It seemed that everyone on the internet back in those early days had business being there and knew what they were doing for the most part. Now the whole world's on. Amazing.