I've had the same problem. It is a different part of the brain you're trying to access. Just like the rub your stomach and pat your head at the same time. I've had the best luck by starting with a simple song on the guitar that doesn't take much to play. Start with something with simple strumming and try sing along to it. Like "Mary had a little lamb" for example. Then as you get better, start adding difficulty to the guitar parts by arpeggiating, adding riffs, etc. while singing.