"1)the problem is likely to be a faulty stick of RAM?" Possible, but did you make sure it was firmly inplace?
"2) can I just put the new stick of RAM in the only spare slot, without disturbing my existing RAM?" Try it, it won't do any harm, either it works, or not.
Just been on the matsonic site, not very helpful, the crucial site had more detail on what you can and can't install. Unless you brought a stick outside of these parameters, DDR memory with support for DDR PC2700,DDR PC3200,DDR PC4000 speeds, then it should work.
I'd def try installing the two original sticks in their original slots, boot up to make sure everything works, then install the new stick in the empty slot.
Hope this helps.