Intermittent Starting problems

My 99 2.4L sunfire makes a horrid buzzing noise under the dash and from the fuel pump relay when I turn my key to on, and the car will not start sometimes I notice that the security light is on, so I let it sit in the on postion for 10 min then I turned it off then tried to start it and it started, but its doing it again. Would this be a connection problem? I tried playing with that relay and swapping it but it just does a buzzing then stop and then buzzes...like its something up in the dash buzzing also, so I play with the neutral safety by switching gears(auto) and playing with the steering adjustment and the brake pedal also, I did notice it almost seemed like the brake would not let me shift it when I was gonna try to see if the neutral safety switch had something to do with it. Been doing this for about a month, and if I bring it to the shop they will replace like 4 things or something stoopid or tell me there is nothing they can do if it works. Any ideas would be appreciated thanks!