I wish I had better news for you, but I think the battery is dud. These modern lithium ion batteries lose capacity as they sit on a warehouse shelf awaiting sale - a battery will lose at least 10% capacity if it's not sold for a year. Given the time-frame since you purchased, you should be able to get a replacement or a refund.
If you bought it from Dell themselves I would go for a replacement. If not, I would try to get a refund since the replacement they send is very likely to be from the same batch (and therefore as old) as the dud one you just bought. Batteries remain an inhibitor to long-term laptop portability/viability.
You are lucky if they last past 18 months and replacements are very costly (for example, a branded Dell battery may cost up to one third of the original laptop cost). Also after you have replaced the battery a couple of times, there is such little demand for the component that you are likely to be purchasing one that has been sitting on that shelf for a while!
If you can, try putting it in a different laptop to see if it will charge, so that you can rule out the possibility of a bad battery. Outside of that, here are a few other things that could be going on... Check your charging/power cable. There could be a problem with that, such as a short.
If it is not that, it may be that the power or charger board within the laptop is bad. In this case, you will have to send the laptop in for repair.
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