Cooling mode (low and High) work intermittantly or not at all. Fan still blows. Husband says there is no filter to be concerned about. Don't use it all the time but would like it to work on demand. It is over 10 years old and no maintenace.

I would have someone take it out of the window (if it isn't already) and with a water hose - wash both coils, (if you use a pressure nozzle be careful to not bend the fins on the coils). The coil at the back of the unit is called the condenser coil, and the one in the front is the evaporator coil, (do not get water in the fan motor or where the switches and wires are located - wrap with plastic/tape or something to keep water out). Try to keep from tilting unit on it's side or upside down, but if you have to (and you might in order to drain water from unit), just do so for a short period. Don't leave the unit on it's side or upside down while it dries out. Let it dry really good and do not try to start unit for several hours especially if you had to tilt it on it's side/upside down.
Once you've washed both coils really good and the unit has dried out - you can buy 'washable filter material' (Home Depot/Lowe's) that you can 'cut to size' and install on the front (evaporator) coil. The filter goes 'in front' of the evaporator coil (sometimes it slides into the inside of the plastic front cover - but in any event the front cover helps to keep the filter in front of the coil) - the idea is for the filter to catch dirt/hair and whatever - before it gets in the front (evaporator) coil and clogs it up. (NOTE: the reason you must have a filter in front of this coil is that the fan motor is drawing air from inside the cooling space, and through the coil.
You should always keep the filter clean which will keep your front (evaporator) coil clean. If it get's clogged with dirt, hair and etc - it will affect the operation of the AC in a very negative way.
As for the back (condenser) coil - it will usually stay fairly clean although you need to keep a eye on it and keep it clean - but, in general it does not need the careful attention that the front coil requires, and "does not" require a filter.
I would then look and see if there is a place (probably not) to oil the bearings on the fan motor. If you do have oil spouts on the bearings (of the motor) be sure and put a few drops of oil in each of them. As I said though, most motors are 'oil-less' these days - even 10 year old units.
After doing all this - you've done about as much as you can do - and you can either put it in the window and hope it works ok (which it might) - or you can have a serviceperson check it out for proper operation. If you look in the newspaper/craig's list - you might get lucky and find a 'retiree' who works on window units and if you take it to him/her you could probably get it checked out for a reasonable charge.
It is doubtful that you have a 'refrigerant problem,' since you said it cooled part of the time, and as for the 'cooling mode working intermittently or not at all ' I'm thinking it might work ok - once the coils have been cleaned. Something else to consider is that the 'speeds of the fan motor' are so close together - it might be hard to tell 'low' from 'high' speed when in the cooling mode.
I don't know how much trouble it would be to put back in the window and try for proper operation and then take out (if it didn't work right) but I think I would try it. Or, you could just try it in the garage or someplace before putting in the window. In any event - from what you've said - I think it's worth a shot to clean it up and possibly have a serviceperson look at it - especially when you consider the cost of a brand new one. The 'important thing' you said was that it 'cooled' at least part of the time, which tells me the compressor (the most expensive part of the AC) is working ok.
Hope this has helped.