"...308 converted..." A great deal depends on how that was done. The original ammo was the 7.5 x 54mm. (The only similarity between those is the bullet diameter and the similar ballistics.) The 7.5's case length is longer by 111 thou., so you can't just ream the chamber. If whoever converted it did so with a chamber insert like that used by the USN on their M1's, those tend to come out.
The .308's shoulder is larger in diameter than the 7.5's by 8.9 thou. If there was an insert that came out .308 ammo would not chamber.
However, chambering around(sounds like it did considering you fired 10 with no fuss. Can you still chamber a .308 and easily close the bolt?) and it not firing indicates the possibility of a broken firing pin.
This is all text only, but it's better than nothing.
http://www.texastradingpost.com/mili...s49manual.html
If it was 'converted' by Century Arms(you didn't say), they are notorious for not having any kind of QC whatsoever.