My BIL is a paralegal in biglaw and he makes good money with all the overtime he works. I am thinking about going on the websites of, say, 20 law firms in nyc and seeing if they have a thing where you can submit a resume. However, I am concerned with the fact that I already have six years of full-time experience, am a little older than a recent college grad, and that this would be a career change for me.
Anyone have advice on how to write a cover letter that addresses my past professional experience and the fact that it has nothing to do with law? Is that fact going to be a big problem? Any input would be much appreciated. Thanks

(edited to take out too-detailed biographical details)