I also got started on computers before the internet and didn't actually visit my first website until eight years later. Initially, the concept of the internet intrigued me, and there are plenty of opportunities it gives us for information, business, discussion, even dating...but I often do pine for the pre-internet days of computing.
For starters, a lot of people tend to think computers are worthless if they don't go online. I have several computers that I either don't take online or only connect sparingly. Most are older, of course, but they manage to continue to be productive for me.
This is because there is quite a bit of software you can actually use offline. I know a lot of people point out word processing, which is definitely the number one use for offline computers, but don't forget graphics programs, spreadsheets, audio and video editing software, games, and programming tools.
You younger folks may not believe it, but we got plenty of work done on those systems. They can still be very useful provided you don't have to email any work, don't rely on the cloud, don't need any sort of messaging or video conferencing software, and don't care about visiting random websites.
I still use offline computers with the children I work with. They are quite old now (it's a "lab" of Classics, SEs, LCs, an early PowerBook, and a IIci) but the programs on there are actually superior to most newer educational programs I have tried. For one thing, they're customizable, often more so than the "fixed" nature of apps or online tools. They are also more polished. Yes, the graphics are simple, but if the main objective is to learn, we don't need flashy animation or distracting videos. There's no annoying music, no ads popping up, no passwords required, no worries if a connection goes down, and no concerns about a student clicking on some other website, either accidentally or on purpose.
A lot of the students, all of whom have never known a time without the internet, will often ask me how they can get online on the computers. I simply tell them that these computers don't go online and that they have all of their programs (they sometimes will call a program a "website") already on them. Sometimes, it takes them a little while to catch on to the concept, yet I've found kids continue to enjoy classics like Word Munchers, OutNumbered, Math Blaster, Midnight Rescue, Kid Pix, and others from the late 80s/early 90s. In fact, they soon become attached to these programs and WANT To learn with them!!!
On an unrelated note, it's great to see the kids figure out the menu bars on the old computers. They all will do a single click and expect them to stay down like they do on any modern computer--yet they all figure out you have to hold down the mouse button on their own after a little trial and error.
Back to the original point, yes, computers are still valuable without the internet depending on what you use them for. This also goes to show that an older computer can sometimes still be extremely useful as long as the programs used with it continue to be relevant to the application. I know there are a few other educators who continue to swear by older machines (I actually know one who still uses a IIGS in her classroom!) which cannot go online.
On a final note, I should say that I don't use old, offline-only computers exclusively with my tutoring business. Some of the older kids do get to use a connected laptop to do research, and I conduct online sessions from modern hardware. My business also maintains a website and does plenty of correspondence by email and text (yes, the parents have all taken to text, which works great since the voicemail feature of the iPhone is so clunky--even the old tape-based answering machine my family had in the 80s worked better). Still, the offline computers are actually the biggest difference makers when it comes to supplementing education with technology, and it's all because of the continued use of software that will never require a connection--which is the key in determining if any computer is still valuable offline.