No Power

Is the LED powered on that is on the side of the AC adapter?

I would also check the battery.

Should be able to replace either of those items cheaply via Dell spare parts or EBay.

If you determine that the power strip is good, the power cable is good, it's very likely that either the power supply or power button is bad.

I've seen more supplies good bad than switches, so I would start there.

If you feel up to the task, the following article walks you through opening the power supply and checking the fuse.

Warning: This can be a dangerous task and if you are at all concerned about your abilities to work around electricity you should buy a new supply.

https://www.techrepublic.com.com/5100-6255_11-1053277.html

This article walks you through wiring a power switch:
https://www.techrepublic.com.com/5100-6255_11-1053276.html

The easiest way to test this is try to find a known working DELL power supply to test your pc with. Remember that Dell power supplies manufactured between 1998-2000 do not follow the industry standard pinout UNLESS you have a Pentium 4. You could do some serious damage if you plug the wrong power supply into the motherboard. If you cannot find another power supply to test your pc, you could purchase an ATX power supply tester (assuming you have a Pentium 4) for less than $10 at most computer supply stores. If you do not have a pentium 4, and your pc is older than 2000, you can test the pins on the motherboroad connector with a multimeter. Here is the standard pinout for the older dells:

1 +5V Red
2 GND Black
3 +5V Red
4 GND Black
5 Power_Good Orange
6 +5VSB (standby) Purple
7 +12V Yellow
8 -12V Blue
9 GND Black
10 GND Black
11 PS_On Grey
12 GND Black
13 GND Black
14 GND Black
15 -5v White
16 +5V Red
17 +5V Red
18 +5V Red
19 KEY (blank)
20 +5V Red

First, check the simplest thing. Try a lamp that you know works into your power strip. If the lamp works, you know you have power that far.

Since you can get a power supply from your local computer store for about $30 or $40, see if you can buy it with the understanding that you can return it if it doesn't solve your problem. It is about a 10 minute operation to replace a power supply. OR. . . you could spend a couple of hours troubleshooting.

Good luck.

Craig Herberg