No. Just be aware of situations that can create a static charge and avoid them or touch a metallic part of the case before touching any electronic circuitry. Been building computers for over 30 years and lots of them, never used a grounding strap, just common sense. No fur socks on acrylic floors and the like.
Unplug the power from the wall, try and power on the PC again (should/will drain the system), then make sure to touch a bare metal part of the chassis before removing anything. I have yet to fry anything (only have 29 years of experience though, not > 30).