^^right on. gapps are proprietary so devs (most) leave them out of their roms for fear of being served a cease and desist order from Google's lawyers. Yes, if you factory reset you will lose (wipe) everything but NOT anything on you internal sd card (your nandroid backup(s), download folder, anything backed up by a launcher, Titanium Backup/My Backup Pro, etc). I suggest you dirty flash your rom and gapps again. Doing this you won't lose anything. Just wipe cache and dalvik cache (don't wipe data/factory reset or wipe system), flash your rom and gapps package again, and reboot.
If you're still having an issue do a full wipe/clean flash at that point. That's not nearly as much of a hassle as some would make it seem, especially if you backup/restore via a laucher (nova/apex) and also TiBu or MBP for apps/data. Google saves your contacts, photos, bookmarks, wifi passwords, and auto restores your apps. Occasionally the auto restore doesn't work for whatever reason so I keep backup of all the apks/data using MBP. Usually only setup my email accounts and Wallet. Aslo, if you use wallet, don't back it up. I always either reset it from inside the app or clear data and uninstall in settings before flashing a new rom. Then install the apk (if it's not in the gapps package) and go through the setup process. It still remembers all your info from the cloud. Apparently some have been unlucky restoring it and borked their secure element.