Can anyone tell me why my new window unit airconditioner has stopped blowing cold air?
There's a lot to address here. So here goes:


In general, when a store is selling a warranty, it is generally going to be a waste of money, FOR YOU, to buy it.
FROZEN: Air conditioners can freeze up, this is often due to things that affect the units performance or refrigerant levels in the unit. Since you keep the unit clean, and you aren't indicating you use it in an inappropriate environment or manner, in general you should be ok here. Nonetheless, things happen, and if the unit freezes up, you can usually tell. Not to mention, you will most likely notice the airflow is not "normal" (if it is frozen)
DIRT: If you have pets, or live in an area where a lot of dust, hair, or other debris could have entered the unit, then the coils could be clogged. So question: what type of "stuff" were you cleaning off of the filter? Did you run it without the filter? If the filter looked like a dryer lint trap, then there is a good chance so does the coils. You may be able to inspect the coils with a flashlight. You could potentially pay someone to service it if you do see dirt inside the unit. You can buy a "comb" for cleaning the coils but its not really recommended on a home unit.
COMPRESSOR/SWITCH: With the unit off, turn it to fan only. Then toggle it to COOL. Does the unit actively draw more current? Do you hear a motor/pump engage? It should be near instantaneous when you turn on "COOL". If you don't hear these things, it needs to be serviced. Unfortunately these are not often worth paying more to fix. It can be a thermal-couple, bad connections in wiring connector or on a board, a fuse, a startup capacitor, low refrigerant due to a leak in the closed system, or a burned out or seized compressor. Parts can range from a few dollars, to hundreds. Then there is a service charge. I would call around to repair centers and see who, if any, in your area will do a free quote.
WATER: Condesate, this is meant to drain right out of the back of the unit. This is done by "simply" mounting the unit in the window with the correct tilt to the unit. I would not anticipate an incorrect incline to ruin the unit. I would expect said improper installation to cause window, window sill, wall, floor, etc. damage, and it would rust out the inside of the A/C prematurely. But it shouldn't stop the unit from working. Using a level and making sure it is in the window properly should suffice. Just exercise safety and caution.
FORTUNE: If you paid a fortune for the unit, what is the manufacturers warranty? Probably a year? If so, it lasted it's year. I am not trying to be cynical, but there is truth to this statement: Businesses absolutely design equipment as inexpensive as possible, while lasting as long as they state it will. Some call this planned obsolescence, and if anyone ever tells you there is not such thing, they aren't entirely correct. My best advice answer here, is to do your homework when you buy a unit, look at various reviews, and only buy once you are reasonably certain the unit you are purchasing is a good deal, (be it value, money, warranty, etc).


On my answer #1 above: Warranties are sold such that the guarantor has "written the fine print" to potentially deny all claims, with the exception of very few. It's a headache often not worth it. So While I'm suggesting you never buy extended warranties, obviously there are situations where it is a good idea. Read fine print, consider cost of a new unit, and if its worth the "value".

Sadly, home A/C units are not high quality.