Well, we have the same OS and cable modem in common (my modem connected via USB ).
I am not sure or clear on what you meant when you referred to your comp and modem stopped communicating other then my own experiance that I mentioned that at times the internet connection can not be found
IF power is restored to the modem
after the comp has been booted up. As I said, for me refreshing and then powering up the modem first and then booting comp always corrected this. It is possible that the "recommunication" process you were talked thru involved changing something in your settings?
If we have the same model surfboard you have 5 status lights and a standby button on the front, if so, do you ever use this? The reason I ask is that little button(which I have no idea why it is there or what its true purpose is) was the cause of the only major problem I experianced with my modem. I have had my cable internet service and this modem for about 2-1/2 years now. When it was initially installed I was instructed by the installer that the standby button was used to turn the modem on and off or when you didn't wish to have an internet connection( for the paranoid people ?). This was incorrect and I began experiancing frequent disconnects and had to reboot to regain my connection. At first it was just an inconvenience and I thought that the cable provider perhaps ended connections that had been idle for a given amount of time in an attempt to preserve bandwith and allow active connections higher speed. When it reached the point of ridiculous I contacted tech support. After a few questions I was told I had been instructed wrong and that the only proper way to shut the modem off was to unplug it. I was told that unless for whatever reason I may feel the need (ie: gone for extended periods like vacations, thunderstorms or not being comfortable with an always on connection) there is no need to turn the modem off. The tech person explained that every time I used the standby it remained in the memory of the modem and basically over time overloaded and confused the modem, the modems response was to end the connection. In a sense telling me something was wrong. This is when I first learned of the method of resetting or refreshing the memory by unplugging and it did correct my problem.
As far as Win98 goes it has always seemed to have a peculiar trait of being problamatic with locking up or not responding at startup, shutdown or both at times. The odd thing is some rarely encounter this and for others (myself included) it is frequent. There is much debate (with threads found here) on the pros and cons of whether it is better to leave a computer always on or if they should be shut down when not in use. Mostly because of the startup or shutdown issues I experiance I opt for the always on and only reboot if I have to after a lockup.
It is beneficial and Win98 does seem to run much smoother if you keep it as tidy as possible by defragging, clearing history, dumping files and cookies from internet temp files, dumping windows temp files and the recycle bin.
When you said your computer would only start in safemode no matter how many times you restarted, did you not get a prompt window telling you why and with the option of how you want windows to start ? Normally I believe that is what I get, with the option of "normal" to bypass the safemode.
Also,here is a startup trick that I discovered that works for me (don't ask why ?) If windows seems to be loading slower then normal or seems to hang at a particular point hitting the enter key repeatedly or holding it down seems to kick it in the butt again and speed up the process. Also, if it enters the bluescreen scandisk automatically (for what it says was an improper shutdown or any other reason) hitting the enter key will also end this task and proceed to load normally. It may bring up the prompt window then asking how you want windows to load at which time just click normal.
As far as the HJthis log, it certainly wouldn't hurt anything. To be honest I don't have a clue what the HJthis experts see or look for in those things

The people that review them seem to enjoy doing it and it is something I would like to learn one day
You could try posting it in this thread to see if someone picks up on it and if not you could try directing someone to this post by posting in a thread used for HJthis logs.................or start a new thread.
Sorry that this has mostly been advice from my personal experiance but I hope you find some use in it for your problem
jjb