iPhone has just died. What should I do first?

Hello all! So my trusted 1st gen iPhone just quit on me two days ago! Have had absolutly no problems for the last 2 and a half years. I missed a call that I felt in my pocket, then about an hour later I tried to check if they left a message... nothing!!

After reading through the questions and answers I feel that checking the battery with a multimeter would be the next step. I have already tried restarting (no luck) and it doesn't come on while on the charger either. Is that correct, and if that checks out what could the problem be?

Thanks

Clint