I have a laptop with W98. I also have a double problem. First, Many times when I start the machine up and see the screen, the mouse cursor goes haywire and the screen is blinking all over the place. I then unplug the mouse adaptor from the port and replug it in, then restart the machine(all this maybe 5-10 times) until I get normal mouse function. It seems that the flat USB port won't work for the mouse, so I use the adaptor, then plug it into the round port.

Secondly, My task bar has disappeared completely from my screen. I had dragged it from the top to the bottom, then it just disappeared! How do I get it back without having to re-boot or turn the machine off?

Press the "windows" start key on your keyboard, should be between the LH ctrl and alt keys. That should bring up the start menu and the taskbar.

Once the taskbar is shown, right-click it and select unlock the task bar. If the task bar disappears again, press the windows key again. Move your cursor to the top of the task bar, only to the point where the cursor changes to up/down arrows, click and then drag it upwards to change the width. If that works, then lock the taskbar, so it doesn't change.

Since your are using a PS/2 adaptor for the mouse, make sure your using the right adapter. It is the one that came with the mouse right? It should have a mouse icon on it.

To use a USB mouse in Windows 98, you need to install the mouse driver, did you do that?

When was the last time you did a fresh install of Win98. Sounds like it's seriously cludged up and needs a good blow out.
Time to back up ALL your data and reinstall from scratch.