2004 hard to start
 

Hi -

I have a 2004 Mini with 56K miles. Recently it has been
hard to start, having to crank it several times before it will fire.
I have to turn the key off and on several times. With the door
open you can hear a faint buzzing sound.
The battery and alternator were replaced about a year ago and
check out fine.

Any suggestions on things to check as cause or check?

Thanks in advance for any suggestions, Tom