If what you're writing is that two Dell OEM adapters are not recognized by the system, then then next suspect is the DC input jack.  That may be replaceable at low cost depending on the system model, which you will need to provide if you require assistance.

If the adapter you recently purchased is a brand new OEM Dell adapter (did you purchase it from Dell) then a couple of things to consider. It could be that the DC jack on the laptop has a broken or bent centre pin, or the charging circuit on the MB is at fault. You did not post the exact model of your laptop so it is also hard to say if the battery may also need replacement.

EDIT: I need to improve my typing speed skills as @ejn63 always seems to surpass my reply speed.

Make certain there isn't dust packed into the center of the charger's connecter, as well as the corresponding receptacle on the laptop. If so, be careful when cleaning the dust out so as not to do any damage.

Thanks for the responses. Sorry, I should have made it clearer. I have bought 2 OEM Dell chargers over the past 4 months (new puppy chewed cables). The first worked and normal functionality resumed immediately, the second was not recognised (have pop-up messages displayed when I turn it on) and the laptop (Inspiron 3585) is unworkably slow and cannot perform some functions. I am 99% certain that this is the issue rather than any other technical problem. I would try another from Dell except that customer service was, frankly, terrible and I am concerned that the next one would be the same. So feel like I have no choice but to buy another laptop.

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[...] the laptop (Inspiron 3585) is unworkably slow and cannot perform some functions [...]

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Try using Task Manager to suss out any bottlenecking. The system disk maxed out close to 100% often causes sluggish performance. For which there is a solution by upgrading the disk.