Check if the light is lit at the plug end of the AC adapter or on the adapter block. And see if that light remains lit when you plug it into the laptop's jack. You said that a power plug light is on, but I don't know if that is on the adapter/plug, or on the laptop. If you have or can borrow another Dell AC adapter of at least 130 watts, try it. It could be that the charging jack needs to be replaced. First, I would try some other steps. Examine the main battery. That laptop is ten years old. If that is the original battery, it's at or near death. Even if you replaced it once, the replacement may now be pretty much dead. Worse, it may be swelling, which can damage the laptop. If there is any sign of swelling,, you must remove it and safely dispose of it.Swollen Battery Information and Guidance | Dell Canada If the list of steps doesn't allow booting does nothing, then I would repeat steps 1-4, and then remove the CMOS battery (coin-cell battery). After 30 minutes, replace it with a brand new coin-cell battery. Then connect the AC adapter and try to boot. Follow the disassembly and reassembly steps in Dell's Owner's Manual.Look on YouTube for videos showing disassembly of your model. But, be cautious with them, as some use steps or methods that are not appropriate. Use the videos to add to your understanding of what to do, but follow the steps in Dell's manual. Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. It's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard. EDIT: I see ejn63 posted as I was typing. dclark15773, you've now got some work to do.  
I have an old XPS-15 9530 that has been working well.  After using it yesterday, today will will not turn on.  It is plugged in and the power plug light is on indicating it is being powered.  When I push the power on button nothing happens.  No lights of any kind, no response of any kind.  Is there any way to get it to work?  Is it likely to be the power button?  Can it be repaired at a reasonable cost?  
XPS-15 Will not turn on