Hi,
Is the old adapter still functioning? If so can you try it to see if the battery now charges or that it is recognized by the laptop?
Can you test the new adapter with a DMM (Digital Multimeter -Voltmeter function) to prove that it is supplying 19.5VDC.
Here is a link to the service manual for your laptop. You may wish to use it to show you how open the laptop so that you can inspect the DC input (Adapter connection port) to see that it is still connected to the motherboard and has not been 'loosened' by use over the years.
http://downloads.dell.com/manuals/all-products/esuprt_laptop/esuprt_inspiron_laptop/inspiron-1525_service%20manual_en-us.pdf