I have an OLD Top loading heavy GE washer which is manual.I do not know the model #.The last cycle of rince and wash does not function.Also the cold cold cycle of water does not function and water does not come in the machine.

Hi from retired Englishman in SW France,

Water first!
If you have checked that the hot and cold water taps are turned on fully and the hoses are not kinked or squashed at the back, it is worth while checking both the hot and cold water inlet filters. Turn the taps off and remove both hoses at the washer end. Inside each inlet port there is normally a little filter which should just slide out. Clean if necessary and replace each one and the hoses. If after turning the taps back on there is no improvement, the problem is symptomatic of a malfunctioning hot or cold water control valve. Sorry but it needs a service call and a check that it isn't the control PCB ;-0(

Suspect blocked filter/drain motor

I would gently suggest as a first step that you clean the drain motor/pump lint tray/filter. So many 'faults' are caused by blocked filters and many machines will not even go to rinse or spin or release the door lock if there is any water still left inside.
Following are my complete and generic guidance notes for checking both the drain motor filter and the drain motor ;-0)
REMOVE POWER AND ENSURE YOU HAVE A WATER RECEPTACLE/RAGS TO SOAK UP THE WATER WHICH IS BOUND TO POUR OUT (alternatively use a wet vac as sensibly suggested by VinnyB1234!)
If you are unsure where the filter is, it is often behind the front lower (kick) panel (or in some machines at the rear in an awkward position!). These panels are either held on by (plasic) screws or will just pull off. Most filters are held in by a round cover/knob. Sometimes the filter will not come out with the cover and you will have to persuade it to come out to play.

It's surprising what people have found in theirs! It is always worthwhile checking it on a regular basis.
Now- whilst the filter is removed it is normally possible to see the drain motor and ensure it is not jammed by a foreign object such as a needle or a toothpick. It should be able to be turned by hand/finger- the power IS OFF!
At this point it is also possible to test if the motor works. No clothes or water in the machine, select a spin cycle and put the power back on. You should be able to see the motor turning at some point, possibly straight away. Using something suitable like a glove see if it is easy to briefly slow the motor down. If it is easy then the motor is malfunctioning.

If these have assisted you please consider a 4 thumbs up for the rating.
Thanks and good luck,
John C