tbh it'll probably be cheaper to buy a new power cable than a multimeter,
unless you're planning to use a multimeter for future projects and you're
happy to buy a power cable anyway if it gives you a negative result! :D
The most common cause of power problems in ye olde laptops (in my experience)
is the battery. They're usually the first thing to go in an old laptop. A
good indication is if it doesn't hold a charge when you remove the power
cable or it drains really fast.
Do not buy a "reconditioned" replacement for it as that will probably be
around the same age as the one you have now and will have a limited shelf
life. Look for an after-market "replacement" battery on the usual online
shopping sites. Just be cautious about the usual things (i.e. sellers with
low feedback, unfamiliar brands, etc).