My best guess is either your atty isn't connecting well, or your battery isn't completing the circuit well. First things first, this is going to sound really stupid, but the very first thing you should do is make sure the battery is in the right way around. In most devices the positive side should be at the top, and negative at the bottom.
Now that the really simple stuff is out of the way, check the atty. When you've got a problem, it's usually something to do with that. Look at the atty connection plate on the device. Most of the time, in most devices, it'll sit on a floating gasket. It may have been pushed in too far to make a good connection. This is EXTREMELY common. Try using a bent paper clip, tiny flat head screwdriver, safety pin, anything like that, to pull it out a bit...carefully. Next do the same thing with the floating gasket that sits on your juice delivery system. If that works, don't screw the delivery system on so tight next time. You don't need to crank it down. On to the next common atty problem. You may have a short or a popped atty (broken coil). Though not as common as a pushed in connection plate, it does happens. Try a different device and see if that helps. If that doesn't help at all, I'm looking at the specs on your device and it says "battery safety protection" in one of the features. I'm assuming that means the device won't let you vape an unsafe resistance at an unsafe voltage for your battery. This may very well be your problem. What resistance are you using and what voltage are you trying to vape at? If you're cranking it all the way up with a low res coil, that's probably your problem. If you want to do high voltage, you need standard resistance, something around 2.0. And if you want to max out the voltage, you're going to want 3.0 or higher. This is a good thing. It will keep you safe. So check that out.
Now if none of that works, go for the battery. It's a telescopic mod right? First things first, play around with it a bit. Screw and unscrew it. Make sure it's twisted fairly tight. I have a telescopic mod (but mine's mechanical), and I had a lot of trouble at first (just yesterday in fact) getting a good connection to the battery. This may be your problem as well. If that doesn't work, move on to the connections. Look at the ones inside first. Does the connection plate look alright? Maybe dirty? Maybe it's pushed in too far. I'm not familiar with your device, but most sit on a floating gasket that can be pushed in too much. It's also entirely possible that your battery is a dud. Try the other one. As for the difference in battery life. You have a variable voltage mod. The higher you crank the voltage, the shorter your battery life.
But it's possible the batteries are duds. Or there may be something wrong with your charger. This is where a multimeter comes in handy, even if you don't have a mechanical mod and aren't running low res/subohming/rebuilding (in that case you want one to make sure you aren't going to blow your face off). Go to Harbor Freight if there's one in your area and get a cheap multimeter. Actually there's a coupon floating around right now that'll make it free. If you don't have one in your area, you'll have to pay a little more. Or raid your dad's garage; dad's tend to have them lol. Check the DC current (on the 20 setting) and see if your battery has any power. This will tell you whether or not it's the battery itself. It should read around 3.7. If it doesn't (and be warned cheap multis will be very fiddly), and you get nothing, or it reads anything significantly lower than that, it's your batteries or your charger not functioning.
If all else fails, it's possible that you may have fried the on board computer. Have you had any serious leaks? It's not common with high quality gear right off the bat, but it is possible that the connection plate gasket may have leaked. I did that to my Lave Tube years ago. If you can't get it working, hopefully you have some sort of warranty and you can get a replacement.
EDIT: Sorry I didn't see you'd fixed the problem. But I'm going to go ahead and leave this up for future reference if you have another problem.
)..your mileage however may vary! 
