128mb of ram is fine for windows 98 and I dont think that adding more would cure your problem.
It could be that the ram has developed a fault though or it could be something running in the background that you are unaware of or something conflicting.
Unfortunately all these things arent that easy to check without access to the pc.
Have you run the various adaware and spyware removal programs and your anti virus, just in case they can spot something nasty thats got on your pc ?
As Dave suggested earlier, a 300mhz pc is a bit old to think about spending much on either by repairing or updating it and if you can afford a better specification second hand pc then I think you will get better value for the money spent on that.
The only thing that you may find awkard about replacing a hard drive is that sometimes the IDE cables (the wide flat grey ones) are a little short and can be fiddly to manouevre into the correct position to connect them.
There are 2 small screws on each side that hold the drive in and the IDE cable and the power lead just pull out.
You cant get then connected the wrong way round as the power plug is shaped to only fit one way and the IDE cable has a blocked off hole usually that lines up with a missing pin on the hard drive.
If I am just transferring data from one drive to another and then removing the old drive I dont even bother to fasten it back in, I just lie it at the side of the pc away from the motherboard so that it cant short anything out and connect the leads
One thing you have to do when adding a second hard drive as a slave is to check the jumper settings of the master and the slave drive.
The jumper is a small piece of plastic with a connector inside that connects two pins on the hard drive.
There is usually a diagram on the hard drive itself showing where it has to be to set up a drive as the master or slave. Its usually easier to use a small pair of tweezers to get hold of the plastic jumper to pull it off the drive as they are very small.
I hope that this doeasnt sound too complicated as it really isnt that difficult to do
If theres anything that you dont understand then you only need to ask