Your battery has been charged with the wrong adapters, a different voltage with itself. When you're charging the battery while the laptop is working, the battery will not be offered enough current -- it's harmful to the battery, even though the laptop won't run with the battery.
If the charger has the right voltage, but the electric current is lower, several things can happen. The device may start consuming more power. This may cause the charger to heat up or damage it. In many cases, the device will start, but the charger fails to deliver enough electrical current, which reduces the voltage (see Too Low Voltage).
For laptops that run on a charger with a lower power supply, several scenarios can occur. - The battery is charging, but the laptop does not want to start; - the laptop is running but the battery is not charging. In general, if you find such a mismatch, it is best to get a new charger whose characteristics match those of the consumer.
A new battery (OEM from Dell) works if the old battery will not keep a charge. How old is it? You can start by resetting the Microsoft ACPI-Compliant Control Method Battery in Device Manager.
If the charger voltage is lower than that of the device, but the strength of the electric current is the same, then the device may work, but far from its optimal mode. If we remember the analogy with the water flowing in a pipe, in this case we will have a very weak current, which does not supply enough water at the end of the pipe.
(Assuming that since you said 'device' and not just 'battery', that we're talking about devices that have managed batteries in them, which is pretty common now) A very cheap one might overload and burn out. Device will take very much longer to charge.