Did I fry a Sainsmart 1602LCD (not shield, just LCD), HD44780 compatible
For me, it's extremely hard to tell if you did or did not fry a device.
Even if you have the device right in front of you, it's often hard to tell.

You've got two options:

Attempt to diagnose it

First you should try to run example code and follow the "instructions". I believe this product is relatively well documented (/libraried?) and shouldn't be all too hard to set up.

If this isn't working, it's likely the device is dead (given the situation). You could go on and fiddle around with it for hours, which might not be worth the effort.

Buy a new one

This will cost you some money. But if you get the new one working, you can test the same code on your old one.

Tips


First connect the wires, check the wiring and AFTER THAT connect the power. (Especially take care on GND/VCC wiring.)
Use black wires for GND/ground and red wires for VCC/5V.(It'll be easier to manage/spot)
Check the devices datasheets (which pins, what maximal voltage)
Try to use female connectors as power-output. (They don't short everything they touch)
Try to use irreversible connectors.
Don't have loose leads dangling around.
Put a casing/backplate on your Arduino (and/or avoid placing it on metal)
Keep your desk clean, bits of solder, wire, leads or screws may cause shorts between pins.