Hi Sparky

Okay, it would seem the problem is that your water inlet valves are not letting water in, so the machine will not start. Since it spins without water, not having water is not the problem. You will need to open the machine and take off the cabinet, which you can do by following this site.

Kenmore top loader blues (SublimeMasterJW's Appliance Advice)

You first need to see if you are getting 120v to the water inlet valves when the machine is suppose to be filling. Check them with a meter. If they are getting power, then the problem is with the valves and the unit will need to be replaced. I doubt if this is the problem since it is unlikely both the hot and cold solenoids would be bad, but you need to check it out anyway.

If the valves are not getting current, then you want to see if your water level pressure switch is ok. Take off the plastic hose going into it and blow into it as hard as you can. You may be able to hear it click on, and even if you cannot, see if water will now come into the machine. If not, replace the water level switch, and if that does not fix it, replace the timer.

Good luck.