Let's get some terms in perspective. So that you can sound like you know what your talking about. I'll answer your Q, later in my answer. Not trying to be rude, trying to give you some info.
"Fuel Injection" is the system the engine uses to mix gas & air to make power for your cars engine.
Your Q, "could a fuel injection fix the problem" is like asking; "how can I tell if my car is a boy or a girl ?
When an engine "starts", it means it is running. When it "turns over" it means it is in the process of starting.
Give your mechanic a break. He probably has other cars to fix that were there before you brought your car to him, and you'll have to wait your turn.
You didn't say what size motor (4 or 6) your 98 Sebring has so, I'd say it'll cost about $200-$300 to repair. Most of that is for shop labor, a standard charge- you have to pay it.