Why does my adaptor not work

The first thing I would do is get a multimeter and test the actual charger—see if the voltage is in line with the rating. It's normal for it to be 1V up or down depending on the load status, so that's not a concern. Say, for example, it is a 19V adapter. 20V without load is good; 19V is fine. Under load, it should be 18- 19V. If it is below 19- 20V without a load, you will likely need to change the adapter, as it has an issue.

If the problem remains, I would try disconnecting the battery for a few minutes and then reconnecting it—sometimes, that helps with Chromebooks. They generally lack a CMOS battery like a traditional notebook, so disconnecting the main battery is the only way.

If neither of those solutions helps, plug the battery into the Chromebook and check the load voltage plugged from the adapter tip into the Chromebook itself. There's usually an easy way to access the connectors inside the notebook, but if not, you'll need to remove the jack and read it outside of the Chromebook, making sure not to stress anything, as it could break the jack wiring if you flex it too much. Should both of these fail, it's generally a bad motherboard on Chromebooks :-(. Chromebooks rarely end up being viable to repair due to the varying update lifetimes and low initial cost, driving repair as a non starter due to parts cost being as much as newer one with years of software support left compared to an older one which hit EOL years ago on paper and the ones which are just not updated anymore by Google, even off paper.