In your slicing program have you enable the option to print a skirt, this will typically print a border around your part to get the extruder working - you may need to experiment with the length of the skirt if your part is small. Also it can be useful to print the first layer a little hotter to get things moving more easily.
The other thing to look at is whether your print head is too close to the print bed, you can tweak this by doing the calibration but putting a sheet or two of paper between the nozzle and the print bed, this will make the print start slightly higher and would rule out being too close.
