You can test the AC supply with an volt meter. Measure between the outer sleeve and the inner connector. You can reach the inner contact with a paper clip.
Clip leads will help set up a stable connection so you can put it all down on a table before you plug it in.
This won't test the power supply whether the supply will deliver its full rated power under load. You'd have to add a pretty hefty power resistor across the terminals to do that, but it will at least tell you if it's delivering voltage.
One easy test would be to borrow a friend's adapter to see if it will charge your machine. The only requirement is that it would have to deliver about the same voltage at about the rated current. Since you don't intend to use it permanently, iIt doesn't have to be an exact match, just close enough for the test.
If the machine is older, the problem could be your battery no longer holds a charge. You may be able to find a tech who can test that for you.
If you need a replacement supply (adapter), I've dealt with
this guy in West Hills, Ca. He has many replacement models for around $28.
Good luck.
🙂