Need to fix a broken moen kitchen faucet

You need to replace the spout o-ring seals. A Moen #117 spout oring kit. If you have a faucet with a sprayer, you will use all three rings. If uit has no spray, you will use only two.

I have had the cartridge replaced in my moen single handle faucet with sprayer in the end and now it turns off by itself. Any suggestions on the problem

Moen has a diverter built in that will need to be replaced.

use the same steps as when you replaced the cartridge, but this time you will need to remove the spout, there is a small diverter, you will see it when spout is removed.

take this part with you to the hardware store, along with the O Rings from the spout, as they will need to be replaced also

use a non silicone faucet lubricant when putting back together

you may need to get the moen cartridge puller,either moen brand, or brass craft, they can be tough to pull some time's

By "leak in the stem" I assume you mean you're getting water in the cabinet below the faucet. High likelihood is it's the hose - either loose where it connects to the faucet or the sprayer. You can pull it out and check to be sure it's tight at the sprayer. To check the faucet end, you'll need to be under the cabinet with a light. If you don't find one of those connections loose, it's likely one or the other is leaking, due to a hose defect or washer (or missing washer).
The only way to see that is to turn the faucet on full (cold) with the sprayer pulled out and look for a leak in the hose behind the sprayer. If not there, leave the water running (may need another person to hold the sprayer) and inspect under the cabinet with your light for a leak either in the hose or at the connection to the faucet. If the problem is the hose or one of the nuts, it's an easy deal to buy a replacement hose - Home Depot stocks Moen.

Once you remove the spout collar you should be able to remove spout and replace the orings

the white plastic clip needs to be removed. squise the clip together and push it out at the same time should come out fairly easy, then just pull the black piece off.

There is a small diverter valve on the faucet underneath where the hose connects too it needs to be replaced depending on the age of the faucet I usually recommend replacing the entire faucet with another Moen product

You have a bad internal o-ring or the sprayer o-ring is leaking, if you look under the sink turn it off and then turn it back on, if you see it leaking out the center shft where the water pipes go into then the faucet may have a broken pipe or loose pipe. check and tell me where it's leaking at. You can buy kits to repiar them they are inexpensive.

call moen for new cartridge