No,, reformatting will not slow down your PC. If by Reformatting, you mean format the drive wiping it out and reinstalling everything.
What is most likely the cause is,,,,, Something did not install properly, OS,
Driver, Software, something...
Or the PC is that old and can't handle any recent updates you have done, again, OS,
Drivers, Software, something else...
A defrag could cause a problem if a problem already exists. It won't create problems. Nor will formatting.
If there is a problem with the Hard Drive, this could be another cause.
There are a lot of variables. But Running Defrag, or Formatting on their own will not cause/create problems.
Only exasperate the ones that already exist