Download mode didn't work because you updated from JB via OTA to latest update. This happened to me too, I had some problem with my phone and I send it to warranty in this state (with download mode broken) and they didn't say anything they reflashed the firmware.
If you want to fix the download mode, get the LGMobile Support Tool from LG website, install usb driver, open the app and connect your phone to pc via usb cable. Then click "Options" and "Upgrade Recovery", it will reflash the firmware and fix the download mode. But there's one more thing, after flash it will say "ROOTED" in download mode.
I not flash kdz again, phone status is good now, '''covered for warranty''.