Normally when that happens its bc the mosfet starts to fry and gets hot enough that it actually breaks the connection. That's why I said its prob a mosfet issue since you described it as the button would still light up, but has no power output. That's what normally happens when you fry the mosfet on an eGo. Two of my friends had the same thing happen, so that's why I figured it was bc of that since they had the same thing happen. Frying the mosfet is a LOT more common when you use something like a 1.5ohm or 1.7ohm carto on an eGo, but technically using a 2.0ohm carto can cause the same problem, it's just alot less likely to happen, since a 2.0ohm carto doesn't stress the mosfet like a 1.5ohm or 1.7ohm does. But it looks like for your eGo, a 2.0ohm was enough to start to fry the mosfet.
I was going to recommend that you could take it apart and resolder the broken wire, but I didn't bc most people either don't know how to do it or don't have the tools to do it. I resoldered both of my buddy's eGos for them that had the same problem and their both still working fine again.
So I'm glad you were knowledgable enough to try to fix it and were able to bc it's really not that hard to do. Most people just throw them out bc they either don't want to bother with it, or dont know they can fix it. So I'm glad you were able to get it going again, and now you know for the future how to fix one if it happens again
I was going to recommend that you could take it apart and resolder the broken wire, but I didn't bc most people either don't know how to do it or don't have the tools to do it. I resoldered both of my buddy's eGos for them that had the same problem and their both still working fine again.
So I'm glad you were knowledgable enough to try to fix it and were able to bc it's really not that hard to do. Most people just throw them out bc they either don't want to bother with it, or dont know they can fix it. So I'm glad you were able to get it going again, and now you know for the future how to fix one if it happens again