lack of space may or may not cause slowdown... depends what you do with the computer. part of the reason is that when your applications needs more memory (ram) than you physically have, it will use hard drive space (called 'swap space') as ram. this is not ideal sincd the HD is slower than ram, but it works. the issue arises when there isnt that much free space, and then the computer will be constantly reading and writing to the swap space (sometimes referred to as "disk thrashing") which is bad.
for basic use, a few gigs should be fine thugh. if you are still getting major slowdown then yeah check for spyware and defrag (thuogh defrag generally wont help THAT much - may or may not be a noticeable improvement depending on how bad it was fragmented to begin with)