Answer to: My display is showing strange shapes and colors. Could it be cracked?It is quite possible that the screen is cracked. Especially from your description. If it was not for you mentioning dropping it I could have recommended maybe that a cable was loose or that the inverter or video card was going bad. These screens are very fragile, and can even break from torsion when closing the Chromebook with one hand from either corner let alone a drop of a few feet or even less. I would follow the guide on the C720 device page for screen replacement.
Answer to: My Chromebook will not power on could it be the power supply?Yes! It very well could be the power supply, and is actually quite common. Before progressing to a more expensive method of repair purchase another power supply or borrow a working on from a friend to to test with before purchasing your own. It could also be something a little more severe such as the DC-in which with what you described the wiggling it could very well actually be that. This requires a little more work, and some basic soldering. You can follow the DC-in replacement guide on the C720 device page.
Answer to: Can I upgrade the RAM of my Acer C720 Chromebook?Hello Christopher, and welcome to iFixit. I see this is your first question. Sadly the Acer C720 does not allow for you to upgrade your memory exclusively; however, you are able to upgrade the memory to a maximum of 4 GB by replacing the motherboard itself to a model with 4 GB. Follow the guide on the Acer C720 device page for replacing the motherboard.