I had similar problems with a bad 4050 with a different display.
To confirm it's duff, move the 4050 to some free space on the breadboard, connect 3.3V to pin 1 and GND to pin 8. Then connect 5V to pin 3 and check with your multimeter that pin 2 is giving 3.3V. If that one's fine, work your way round each of the in/out pairs and repeat the test for each. Anything other than 3.3V from the outputs and you should put the 4050 in the bin.
I've been having the same problem. I've wired up two separate displays, with two different 4050s. One on a breadboard, and one mounted on an adafruit protoboard.. I can switch between displays, because I used a header on the protoboard. One LCD illuminates with very poor contrast, and the other won't show an image at all.
The failing LCD was showing an image, but it gradually faded.
Using an oscilloscope I could see that the output from the 4050s is correct (at 3.3v). On the clock and data lines I can see the signal when the LCD updates.
I am concerned that there is a poor component in the LCD but unsure how to verify this.
An ohm-meter across each resistor shows correct values. 1k, 200 x4 and 0.
What are the capacitor values?
Is there anything I can do to fix the displays?
PS. I was concerned initially that the 4050 is not rated for 3.3V (the spec sheet show 5, 10 and 15V), but the output on the 'scope was fine.