i started off exactly the same - vocal cords, chords, can't co-ordinate! however with a bit of confidence and practice i would say i am at reasonable sing-song standard, no complicated fingerpicking while singing or anything, but i can play and sing at the same time.
to be honest, it came pretty slowly, i would take a song with simple chords, easy strumming pattern/rhythm and well within your vocal range, and just stick at it. play the chords over and over until you know the song inside out. then just go for it really, it takes time but if i was able to do it, anyone can!
good luck. FWIW, i started with the nirvana cover "where did you sleep last night"