My daughter has an Inspiron 1525 and we just purchased a new battery last week for her straight from Dell. It initially charged up but is now not taking a charge. How do we fix this

First, you need to make sure your power adapter is providing enough power to both run the laptop & charge the battery. A very good way to do this is to compare your laptop voltage & ampere requirements (written on a sticker on the bottom of the laptop) with the voltage & ampere ratings of the power adapter. Voltages should be the same, or the power adapter's voltage about up to 0.5 volts more than the laptop's voltage rating. Amperage of the power adapter should be at least equal to or greater than the laptop's rating. It should never be less than the laptop's rating, or else the power adapter will be providing insufficient amperes to charge the battery. Of course, the power adapter's nominal amperage might be ok, but it degraded on usage. You can verify this by testing using a good or new power adapter.
If the battery did not charge using the new power adapter, take the battery off the laptop, & using a dry tooth brush, scrub in between the fins of the battery connector on the motherboard & on the battery it self, then put the battery back into the laptop & try again.
If this still did not resolve the problem, then the battery itself could be bad. Try it on another laptop, or try a good or new battery in your laptop.
If this did not work, there might be a possibility that the charging circuitry on the laptop's motherboard is defective & needs servicing. In order to do this, the laptop needs to be disassembled & the motherboard checked for defective/burned out components in the area near the DC jack. Any defective/burned out components found should be replaced, or you might need to replace the laptop's motherboard altogether.