Flashing check engine light and car started shaking

Check engine light suddenly came on but it's a like blinking in and out. the car started shaking not like the car needed an alignment but worse more like vibration. so, I got car parked and checked everything that I knew to check and being that I was at the Doctors office I had to try and start car back up and it wouldn't crank. All the lights came on, but it just wouldn't start. I had it towed and somebody tightened my battery cables and car started so I drove it just down the road and soon as I got to 15-20 MPH the shaking/vibrating again so I parked it and again it won't start. brand new battery and alternator as if August. Please, please help!