No, I don't agree with any advice that suggests that there is a problem with the adapter nor with the laptop. First you need to consider the solution that I describe below:
In my experience, the most common reason why an adapter with MagSafe connector fails to light / charge properly is because of '''dirt''' collected on the female (laptop) side of the connector, all along the inside corners of its rectangular outline. This dirt prevents the adapter's male connector from sitting properly and establishing and maintaining a good contact.
Prove this by taking a suspected defective AC adapter and trying it on a new, clean laptop. It works right? The Apple Store "geniuses" do this all the time, without thinking through and realizing that the problem is dirt on the customer's own laptop!
What's the solution? Use a magnifying glass to take a good close look at those inside corners of the female MagSafe receptacle on the laptop, and carefully clean out any dirt that is there. A sharp, thin instrument works best. It may help to use some alcohol sparingly, applied with a very thin, rigid absorbent swab. After it is clean like it was when it was spanking new it will make good contact with the AC adapter connector for another year or two, then repeat the cleaning when it is necessary again.
It is amazing how such a surprisingly small amount of dirt can interfere significantly or severely with establishing and maintaining a reliable MagSafe connection. Also note that buying a new AC adapter doesn't help at all because the dirt collection is on the laptop.