Hi yudopplyr, and welcome to AF.
I'm afraid that /data and /system are rather important: /data is where all user apps and app data (including user settings, contacts) are stored, and /system is the ROM.
Can you still get into recovery (4Ext)? If so then if you copy a custom ROM .zip file onto your sd card (either use a card reader or mount usb storage from 4Ext Recovery and copy over usb) you should be able to install it ("install zip from sd" menu). You should always do a factory reset first, but as you've already formatted /data it may not matter so much (but worth doing, if only to clean up .android_secure on your sd card).
I'm afraid I've no idea what those backup files are, though I'm not familiar with the Desire Z/G2 (I do have an HTC Desire and use 4Ext Touch recovery on that, but don't recognise those filenames). For the same reason I can't recommend a ROM for this phone.