I just bought an ink kit to fill my ink cartridge but the computer screen keeps saying that there is no ink?

The cartridge is chipped. Just adding ink does not reset the chip. There are work arounds for many printers, however I don't know what kind of printer/cartridge you have and can therefore no advise.

Almost all cartridges have a chip inside, once it gets activated to send an empty signal you cannot reset that even if you refill the cartridge. For some models you can find replacement chips. My advice is to just refill and use, refill again when it won't print anymore and disregard the empty warning. You can also get into printer settings and try to disable the empty warning so it won't bug you every time you print something.

Refilling cartridges are simple enough, but at times refilled ink cartridges may work, but mostly not. Most printers will not recognize refilled ink cartridges, once the ink is exhausted, the chip expires. Refilling them may be a costly gamble on your part. So to save you any grief, it may be advantageous on your part to just replace the ink cartridge