Luckily your model is one that can be replaced with a dc jack that is user replaceable and doesnt need soldering.
However, it sounds like you might have an issue with the plastic housing inside that holds the dc jack in place. In this case, do you happen to have experience opening laptops? They are all basically the same. You will remove the battery and all the screws from the bottom, then you remove the keyboard usually by tabs near the top of the keyboard and you unlatch the keyboard connector on the motherboard, then separate the top case and bottom case from each other and make sure you unlatch any cables that are still connected to the motherboard. This is a real quick and not very detailed run down, but if you are comfortable with tinkering with it, you can open it up with a little bit of effort.
If the dc jack is good and it’s just loose inside of the laptop itself, use some decent super glue to hold it back in it’s proper spot. I’ve done this countless times for customers with no complaints.