When screwing the cartridge onto the battery, be careful not to overtighten. Just twist until snug, otherwise you may have connectivity issues.
A common issue that happens with vape pens, sometimes as a result of being overly tightened, is that the metal rings that conduct electricity get pressed too deep and fail to make contact with each other.
An easy solution is to use a paper clip to very gently pry the metal ring up.
Be careful not to break the ring off! It is only attached by a very thin wire. Lift it evenly by only a small amount.
If adjusting the ring on the cartridge itself does not solve the problem, try the same fix with the battery itself. The ring hole is smaller so you may need a thinner paper clip. Remember to be gentle, these are very delicate pieces. It takes very little force to raise the ring slightly.
Most of the time this will solve the problem, assuming your battery is charged and your cartridge has oil in it. Happy Vaping!
Here's a video of the process: