My washer will start with the wash cycle but will not continue on to the next cycle.

You did not say what model you have. Here are some manuals: https://dl.dropboxusercontent.com/u/8010163/Whirlpool-Kenmore%20washers.zip
https://dl.dropboxusercontent.com/u/8010163/Understanding%20automatic%20washer.pdf
You may need a timer.

Might be overloaded or not connected to the right tap

If one of the screens on the water inlet is stopped up, like the cold water, then if you have it set for warm wash it will work until it gets to rinse. Then it will stop. Take the hoses loose from the back and check the screens before doing anything else.

Does it drain after the wash cycle?