Like Waffle said, a fully charged cell should be at 4.2 volts. you have 3 of those, so full charge on the pack should be about 12.6. So in order to know the voltage drop you need to be able to see the voltage you are using. There are a few ways to do this. One is if you have an OSD which displays the voltage in the video feed. The other if you don't have an OSD is with telemetry to the radio. For instance if you have a FRSky Taranis, you can set up a screen on the controller with voltage. Also, min voltage and max voltage.
If you have OSD, make sure your voltage is displayed in the feed. You should see close to 12.6 volts on a full charged pack. When you arm and take off, and throttle up, take note of how low the voltage drops as you raise the throttle. This is your voltage drop. All packs will have some sort of voltage drop. But it's minimal on a good pack. So if you throttle and its still at like 12 volts, or 11 point something then it's not your batt. If you throttle up and it drops to like 10 volts or lower, you have a bad pack. That would be why your quad won't lift off.
Some other reasons..
Props - Upside down props don't provide as much thrust. The also sound weird and high pitched. could be too small props, or not enough pitch but unlikely. Un balanced props. If you have an unbalanced prop or props, because of all the vibration your quad is trying hard to keep you level, so all your motors are speeding up and slowing down like crazy and cant speed up because it's trying to maintain control. You would know this by erratic sounds.
If it's not the battery, and it's not the props, and everything seems to be working otherwise, then you have some sort of config problem. Either with the firmware or the wiring...
Something to look at if you have BLheli32. There is a setting to limit amp draw. If that for some reason is set really low, then it's not letting the ESC's draw enough amperage to lift off. It would have to be set really low, because even when you set this, and you hit the limit, the quad will slowley spin up as the amp draw drops after the initial surge.
You should post vids on youtube and post link. Upload images to imgur and post links here for us to see.
All in all you could re flash and start from scratch on config and insure wiring is correct.