Firstly...

You need to pull a vaccum on the system. To do this you need to have an A/C vacuum pump. If you do not do this you are charging into a moist system and you just destroyed your accumulator/dryer. You changed it for nothing, now you need to change it again.

Likely the problem is that the moisture in the system is freezing at the orifice valve and blocking the flow of refrigerant. Despite the instructions on R134a cans sold locally and such, you CANNOT just open a system up, and throw in refrigerant. You NEED to pull a vacuum to as close as 30 millibars mercury as possible. If not, moisture is in there, it can freeze, block. Also you drier is full of moisture again (this is why the ends were capped closed when you bought it), and the moisture in there will likely quickly destroy your entire system. It needs to be DRY. Pulling a vacuum boils off any and all moisture. It is also a method used to ensure there are no leaks, if the vacuum holds over a period of time. Once the vacuum is pulled and it holds for a good hour, then you can charge the system, with a proper set of manifold guages.

The Walmart kits are only good if you have a 500$ beater car you don't care for.

Get another dryer, if you cannot "flush" the system then at least pull a vacuum, and then recharge. You can charge by weight or by monitoring high/low pressures.

BTW the compressor IS supposed to cycle. This is a sign of a preoperly charged system, on average it is on only 50% of the time. If it does not cycle, then there is either an electrical problem or the charge is not correct. It still can produce cold air though, but at the expense of unnecessary compressor wear.

Keep in mind that R134a charging needs to be very precise, unlike our older cars runnning R12. It is very easy to over/under charge an R134 system.

Regards,
Greg Mustang
Montreal - Ottawa
Canada