Those wrist straps mostly just supply a placebo affect.
Why in the world would you reassemble your computer?
If it's working, then great; leave it be.
If it's not working, then you need to tell us what the problem is. If it were caused by static discharge, it's very very unlikely that rebuilding the computer would help in any way, shape, or form... but it's also very likely that the problem is something easily fixable. (You just have to tell us first.)