Reach out to anyone you know in the music industry, producer or not. Ask them to critique your music to see if you even have a chance. If they like it, ask them for any contacts that they may be able to provide.
Sign up for membership sites where producers can be reached. Hitquarters.com and Taxi.com are great resources for information about producers, A&R professionals and other music executives.
E-mail any producers you feel would help you with advancing the quality of your music. Focus your effort on producers who work with artists like yourself to get the maximum result.
Call publishing companies and record labels and introduce yourself to the various gatekeepers. If you make a friend at a lower level, this may turn into an opportunity to present you music to producers at some point.
Speak with studio owners in your local area and see if they know any producers interested in working with an artist in your genre. There are many local producers who can get your music in the right hands.
Continue to correspond with those who you have connected with regardless if they wish to work with you. They may run into someone looking for exactly what you have to offer, and if you have maintained that relationship, they may be willing to pass your music on to them.