PC connected to a grounded outlet, but connected via an ungrounded extension cord (plug)

Hello beautiful nerds,

I am on the verge of upgrading my pc when it strikes me, that it has been connected to a grounded outlet, but without a third pin in the extension cord - I will offcourse upgrade the extension cord.

But i will need to go inside the pc to switch the motherboard and i would do so on a hard surface.

MY QUESTION IS:

Is it safe to go inside the pc now that it hasn't been properly connected?