Google services won't start. Can I save my phone?

A

AC Question

I'm using an LG Optimus L90.

Here is the sequence of events that led to this:
- Was prompted to get Android 5. I installed it. Never had a single problem with this phone before I did this.
- I tried to download a large game but the download kept failing. After a couple more tries, it suddenly said I was out of storage space. I checked my storage and it said 5 GB was being taken up by "System Data".
- I clear some games to make space so I can look up the problem and get any utility apps I would need. According to the Google research, the problem was with a data folder I don't have access to. I tried the *#9900# code which gave a "connection failed" error, so I was left to either do a factory reset or root my phone.
- I rooted my phone.
- Afterwards, used DiskUsage to check what was taking up so much data, about a fourth of it was Dalvik cache. Google searches instructed me to just go in and delete everything in the Dalvik folder manually, but I was scared to because I didn't want to mess up my phone (the irony). Downloaded System Cleaner ROOT in hopes it would solve it. It didn't, it just messed up all my programs. It set up a backup, so I loaded the backup and things seemed to turn back to normal. However, it did absolutely nothing to fix my full storage problem.
- Backed up a bunch of my stuff to my SD card and went for the factory reset, again thinking it would be better than if I just went and wiped a bunch of files I'm unfamiliar with. After the reset, the phone brought up that "upgrading your apps" prompt before starting. Now nothing works again and I'm being spammed with "Unfortunately, _______ has stopped" messages, including Google Play services, which is required to get past the set-up screen.

I don't know whether it was the System Cleaner app or if it was the Lollipop that screwed things up, but my phone is now useless since I can't get past the "set-up internet connection" screen. Is there anything at all that I can do? Because this is pretty bad.