Unable to open some APS & to sync them. Need factory reset but need to back up calendar first..

A

AC Question

PLEASE HELP!!! My phone, LG G3, got dropped on the floor on December 2015. One of the bottom corners of the screen shuttered. Due to this, the phone started to "freak out" and it'd do things on its own like if someone was pressing buttons, but I guess it was due to that corner of the screen being shuttered that was cause the phone to short circuit or whatever is called. So I got the whole screen replaced. The phone went back to perfect. Everything was great with it, except about a week or two later, certain apps wouldn't open, such as the "google play store" app, my GPS app, and a few others. Some other aps, however, would open normally. My e-mail account also wasn't syncing anymore as well as some other aps. Therefore, I stopped receiving emails on my phone since the email account wasn't syncing. I noticed that all of this started to happened after a symbol appeared right next to my "signal" or "WiFi" icon on my phone; this symbol I'm talking about is a circle formed by two arrows. In other words, to concave arrows are forming a circle.
I took the phone to the store (my carrier is Sprint), and they suck. They pretty much didn't know/do anything, and all they told me is that I needed a factory reset, which will wipe everything on my phone out. They told me to back everything up, and then do it. Seemed easy enough, except for the fact that my most precious possession in that phone is my calendar. My calendar has extremely important info that needs to be saved and preserved, and thus far, I have not been able to figure out how to back all AAAAALL the information that I've saved to my phone's calendar for almost two years now. The catch is that when you put stuff on your calendar on a LG G3 phone, you can either choose to save those events/reminders/alarms, etc. to either the phone, or a Gmail calendar. At first I was saving all to my Gmail calendar, however, it became very annoying because I was getting emails for EACH event/reminder, etc. I had on my calendar, thus, I was being bombarded with emails all day everyday at my Gmail account. So, I decided to switch it, and started saving all my calendar events to my phone. Now I regret it as I don't have them backed up and seems like there's no way to back them up. I started to manually switch event by event from being saved on my phone to my Gmail account, which is tedious and daunting but I'll do it if that's what needs to be done. HOWEVER, since as I mentioned before, my phone isn't syncing anymore, then even if I manually switch all my events/reminders to my Gmail calendar, it won't do anything/get backed up anywhere since it doesn't sync. This is terrible! I CANNOT lose that data.
I downloaded a free software a few days ago, "Wondershare MobileGo", I have a 15 day trial and 5 days already flew by. I already backed "Everything" up to my computer, BUT, I have no idea if the events/reminders on my calendar also got backed up, for which is was trying to see if there's any other way to back my files up, but more importantly if there is ANY way to be sure all the information saved on my LG G3 calendar can be backed up and saved so I can reinstall it back on my phone once I go through the factory reset in my phone.
This is a real issue I'm in and thus far no body has been able to figure out what the heck is going on with my phone or how to help me with my issue.
Can someone here help me PLEASE?!?!.....