My husband grew up around plumbing and now works for a plumbing/HVAC company. He said that it sounds like there is no pressure in the cold water line. The hot water is fine because the cold water fills up the water heater, and then the water heater puts out the hot water. If the cold water has no pressure it is probably because there is a leak in the line somewhere.
The first thing to do is exactly what Tara P. suggested and call your water company to find out if your water usage is higher than normal. If it is then you can guarantee there is a leak in the cold water line. You will need a plumber to come listen and figure out where exactly the leak is in your house, and then remove the pipe that is ruined and replace it.
Right after my husband and I got married and living in our first house, we had a HUGE leak. The utility company showed we had used 72,000 gallons of water in a month! We were wondering why we hadn't found ourselves in the middle of a lake or something. Hubby had his uncle (a plumber) come over and he found our leak. Luckily ours was accessible from the back of the house. It was an easy enough fix, but we still had the water bill to pay. The utility company lowered it a little for us because they agreed that 72,000 gallons was a lot to use in a month's time. We still had to pay a good portion of it though, because the water lines at our house are our responsibility.
Good luck!