This is simply a bad idea unless you just want to try it for fun.
Anyone who suggests it could be done is making too many assumptions. There isn't enough information to make a call.
Probably the main issues include
Win98 is old, is no longer patched and is likely vulnerable to many existing penetration techniques which were not even thought of back when it was last patched/tested. Bottom line, it is a huge unknown and almost certainly has vulnerabilities.
What web server would you run? It is likely you can only get an old web server i.e. old version of IIS or similar due to the age of libraries etc. This means running old server which almost certainly will have significant vulnerabilities.
More effor than it is worth. I suspect once you start trying to get this to work, you will run into all sorts of problems. This sounds like a very difficult task compared to the benefit/result you will get.
Others have focused on the comment that it is too old to run Linux. This is not true. If it can run win98, it can run Linux. It might have difficulty with current distributions, but you could do it with probably the same level of effort, but this is still more effort than it is worth.
Given the age of the system, more than likely, you will put in hours to get it working and then find it suffers a hardware failure. It could be an interesting thing to do as an experiment and learning exercise, but certainly isn't worth the effort if you actually want it to be useful