Yup, do the same check as in the vid, note codes and look them up. Don't forget to post up the codes here as well.
I highly doubt it is the coil as the coil provides spark to all cylinders. I would suggest checking the cap and rotor, depending on condition and/or age, replace it. If the problem persists to the same cylinder, I suggest doing a compression test on all cylinders and possibly a cylinder leak down test as well.
My best guess for that dead cylinder would be either a dead injector, burnt valve or burnt distributor cap.
As far as shops that do this type work, any of the big name tire shops are capable of checking this. I'm just not sure how much each shop charges just to diagnose such problem/s.