I just created me a nice new Ebody armor set, yet I am unable to enchant all of it.
I could enchant the chest and gloves, but after that I suddenly had no Soul Gems available.

I thought I had run out of soul gems so I bought some more, then checked my inventory to see that I had 20 soul gems of every kind, yet I still cannot use them for enchanting.
Why cant I use them?
Is there a limit to how much I can enchant?

My enchanting skill is 80+.

Was the gems filled with souls?

Yeah you need to trap souls into the gems.