The low amount of available free space on your hdd(s) only contribute some tiny amount to the overall lag/slowness of a PC.
Some other factors that would contribute to a slow PC are mentioned above, but i will list it here in short form:
- Crap/outdated technology, not enough system resources available when needed for your PC's level of use and work (eg RAM etc), as well as slow types of technology to start with (eg 5200RPM HDDs)
- wrong BIOS settings, incorrect/outdated/generic drivers used
- HDD/IDE adapters set to PIO instead of DMA
- Installed programs, fonts, startup apps, background apps running, list goes on..
- Spyware, malware and the likes
- HDD not defragged, or cleaned up/maintained or HDD failure eminent
To answer your question, yes a reformat will solve all your problems (not relating to hardware) since you will possibly kill whatever is causing it in the first place in one fell swoop, but you won't know in the end what was causing it in the first place, and whether its avoidable or not.
Have a read of this to help speed things up:
https://www.techspot.com/vb/topic53669.html