Many people harbor an obsession with the notion of older computers being the best for writing, and often maintain that they could only get their writing done on such a machine. (Further, it's typically an old Mac.) This idea is popular on Ye Olde Computer Forum, probably because generating text is one of the few things older computers (Macs in particular) have a lot of success at doing. The public excuse has almost always suggested old computers are a good writing environment because they allow fewer distractions. I don't subscribe to the distraction theory, however, for a few reasons.
The main one is there are always distractions. I don't really think it should be harder or easier to stay focused on a computer with a dozen Breakout clones and the Oregon Trail than on one with Facebook or YouTube. The "fewer distractions on my old computer!" group is hilarious because they are the same people who want to be able to use modern Web sites on said old computers. Even though you can be more productive on such an old computer, because modern web sites do not work on them. I've long thought your ability to focus on a task is really an internal thing, and it's a skill you either have developed, or have not. If you aren't committed to writing something, you will find the System Preferences even more interesting than your writing, and nothing short of locking yourself in a stimulus-free room with a pen and paper will be enough to truly eliminate distractions.
This isn't to say developing habits for writing is a bad thing, but I don't think technology is necessarily the solution in and of itself. On the contrary, I've long found unnecessary use of different technology can be a distraction to what you want accomplish. I find so many people get wrapped up in the "process" of writing they don't seem to recognize their writing is actually terrible. I think it comes down to an obsession with sitting at a particular computer and hitting buttons to create the illusion of productivity. Writing on an old Macintosh where you don't have some of your normal distractions isn't going to turn you into a better writer. Practice might, but I think the actual opportunity to practice writing is lost on a lot of people who end up putting too much time into preparing or planning their environment instead of just sitting down and writing something.
Of course, technology is often a factor, and I'll admit I do a certain amount of what could be called ritualization as well. When I start planning my writing process, I need to make a plan to write at a certain time and place and then follow through. Using calendaring software can help me plan the activities I need to do in a certain period of time, so I have time left for writing, outlining software can help keep my writing focused, and having a very portable computer with a strong battery can help by allowing me to write anywhere. In addition, using a modern computer helps me move my writing around more easily, so I can share it with other people.
If I'm feeling particularly tied to a certain place or my writing destination has sufficient outlets and space, there's no real reason I couldn't use an old laptop for writing, but there are some workflow questions to be answered, and at the moment, my workflow tends to imply something with access to SharePoint sites and has a modern copy of Word on it.
In a way, I think this is pretty similar to people who use WordArt as an excuse to procrastinate from the task at hand. If it takes you 50 minutes to decide on a suitable font and shade of blue for the title of your paper, you have 50 less minutes to spend writing it, but I think most people still feel as though they've accomplished something productive.
Even I develop odd little habits like this, though mind tend to be related to writing.
This kind of stuff is one of the things I like best about the National Novel Writing Month. I only have the wherewithal to do it about once a year, at least for the full 50,000-word goal, but when I'm doing NaNo, I become very well trained in managing the battery on my computing devices, and either synchronizing my novel file to the SharePoint site (and having access to Wi-Fi everywhere) or simply using one computer for all of the writing. All of this is in service of writing as much as possible in the month. I would suggest when you need to dedicate enough time in a month to generate a 50,000 word manuscript, you really do spend more time actually writing, and less time focusing on the technology, or the other habits you typically hold onto while writing.
The other thing I think is odd about specifically wanting to use a very old computer for writing is related to the purpose of the writing. I'm not so sure most people are thinking clearly about the destination of their writing when they choose to do it on a computer requiring at least one intermediary to move data forward to a machine to get it on the Internet. This, as an issue, sort of depends on what technical resources you already have available, but even if you already have a Linux server with Netatalk, I've long found it more convenient (and reliable, especially on mobile computers) to just write on a modern computer with access to the web site you'll be posting on. It's a little different, admittedly, if you need to print your work instead of posting it online, however the need for printing (at least in academic environments) as changed over the years. When I started at the university eight years ago, owning your own printer was relevant, because there was almost always a worksheet to print or something printed to turn in. When I finished two years ago, I hadn't printed a document on my own or to turn in for two years; everything was transmitted electronically and was expected to be in a certain file format.
There are always exceptions, and the recent news of George R.R. Martin writing on a DOS computer is unlikely to help my case. I'm sure somebody, somewhere is still in a situation where their writing is going nowhere, or they have the total freedom to turn it in on printed pages. It would be interesting to know how the Game of Thrones series gets turned into the publisher, and then edited.
Journaling and writing you expect never to publish is yet another situation, but I still don't like that idea, because newer journaling applications and computer systems have better search functionality for keeping things organized in a "journal" format.
Ultimately, do what you like, but if what you like is to write using an older computer, don't play the "distraction-free" card on me. It won't work.