1993 Chrysler Le Baron '93 Lebaron convertible won't turn o

Electrical problem
1993 Chrysler Le Baron 6 cyl Front Wheel Drive Automatic high miles

Dear sirs,
I recently lost the key to my '93 LeBaron. The car sat over the weekend until I had a key made for it. The key appears to be working fine(turning far enough) and the dash lights and battery guage are working. The car will not even turn over now. When I turn the key there seems to be a very faint humming sound, but even that does not appear to be happening every time. Other than that there are no clicks, no nothing. The battery shows it has the same charge it always does, and there is no anti-theft devices on the car. I am hardly an experienced mechanic, but need to fix this on my own for financial reasons. I appreciate any help I can get on this. Thank you for your time, Chris.