1994 Buick Lesabre Starting problem

When turn key I get a Buzz sound like coming from the dashboard. Battery OK, lights will come on fine along iwith all the accesoryies. When turning the key the lights will not dim, just the buzz, that goes away in second or so, minor click. Not like the old cars when you could rock and release, then start, just that buzz
sometimes would get the buzz then back key off, then turn key again and car would start. Now just that buzz.
thanks
Jerry Clarke