Explain why you think the adapter has failed. Have you tested the battery and checked the bios? Do some investigating before wasting any money on the old 2010 laptop. You might not need an adapter. It would be better to replace the computer with a newer model. Here is the adapter for your model-- www.dell.com/.../pc-accessories Consider putting the $70 towards a new laptop.
What is the issue with the existing power adapter?
The XPS 501x is compatible to work with 90W and 130W adapter. Kindly find the specifications here - see page 95.
However, the power adapter depends on the video card - integrated or discrete and memory being used on the system.
Also, please click my DELL-username and write me a private message with the service tag and your Name for case records.
Let us know if you have any other queries.