Car cuts off, won't for a while. Revs without fade, no window, nor locks, dome flickers

In the three years that I’ve owned my car, it’s always started on the first turn. Last week, it didn’t start until the second attempt.



The next occurrence, it started up on the first try, but cut off immediately. I got it to start after a number of tries.



One time on the highway, it had a very noticeable stutter in power, but it kept going, luckily.



I stopped to get gas. It wouldn’t start back up, so I had it towed. It revved and revved, without fade. I couldn’t get the power windows to work, nor the power locks. The dome light would just flicker with every attempt.



The mechanics got it to act like I described. I ended up paying $300 for a tow, testing and a new battery. I didn’t think that was the remedy. If it was, I got off lucky. I drove it about a 1/4 mile and it cut off on me. I had to push it to a sidestreet. Same symptoms: revving like a champ, but won’t start. No windows, nor locks, lights flicker while attempting. This is with a brand new Interstate battery.



The mechanics are baffled. One of them thinks that it’s a ground wire somewhere.



HELP!!!

I would assume the shop would check out the ignition and fuel systems in the search as to why the engine isn’t starting. There may be a fuel relay problem that is causing the trouble. The trouble may also be related to the problem with the windows and door lock trouble so that needs to be checked also and fixed at least.