My dimension 4500 was accidentally powered down when the power strip was turned off and now I can't restart it with the power button. This has happened once before and it started after I kept messing with it but this time it won't do it. There are no lights at all.
Help!

So no way to turn it on? Does the battery light flashes when you're charging the laptop?

If not then you probably killed the battery.

Thanks for the response. My system is a desktop, not a laptop. I did replace the battery, however, but it didn't help. There is a light behind the power button but if I hold it down for about 10 seconds, the light goes out. Then if I push it again, the light comes on but still no power.

No lights at all except the power button? As in on the back the ethernet slot isn't lit up for example? Are fans spinning ? Is there any beeps ?

Replace the power supply unit.
You have a Dell - enough said!
You say its happened once before - so you have had a warning that the PS is starting to fail.
The light on the back CAN continue to glow even with a faulty PS, just means that the cord is plugged in!.
Pressing and holding in the computer power on switch, when the PS is off discharges the residual power on the MOBO (the capacitors).

I took it to someone and he thinks its the power supply and is going to replace it for me.
Thanks for the help.

Your'e welcome Laurel.
Post back on the forum if replacing the power supply fixed it.