2000 Cadillac Deville service security light

Hey I have a question about my 2000 Cadillac deville? I was driving a few days ago and my anti theft security comes on, and stays on until I get to where I was going, when I came out to leave my car wud not start for anything in the world. So I left my car there, The next day I go back to check and see and still nothing, I replaced the starter, still nothing, get it towed to my house. Battery was dead, so I charged it and it finally starts but doesn't stay running, I'm thinking a bad ground so I tighten up grounds and finally get a good ground running to body of car. My car is starting everytime now but the security light continues to come on while driving and mostely when changing thru gears and I feel a jerk. If I start my car and sit there and run thru the gears, whn I get to drive the head lights dim, whn I shift it to first gear the line under the PRD321 letting you know wht gear your in stays under D and the security light comes on while in 1st