Inspiron 546 minitower won't start

Is this 546, 546s or 546 MT?

Is the power supply LED on back of case on or off?

Do you know the outlet works? Have you tried a different power cord? If you use a power strip, surge protector or uninterruptable power supply, remove those and connect PC directly to a known working outlet. 

You can try this:

1. Power off and disconnect power cord from rear of PC
2. Press/hold power button for ~30 sec
3. Reconnect power cord to rear of PC and see if it boots now

It's a 300W PSU. You can check out refurbished Dell PSUs for the 546, 546s and 546 MT here, as one example. The systems use different PSUs, so check the part number on the one you have, and shop around for that part number or its equivalent for best pricing, condition (new/refurbished) and warranty.

And only you can decide if it's worth the money to repair this older system or not...

Following your instructions,

1) power off, press power button for 30 sec.

2) plug in, Green light at the back comes on.

3) Press power button, Green light off and fans spin a few times.

Shipping says this is an Inspiron 546 MT.

Thanks!

Does that PSU LED come back on or does it stay off after you press and fans rev?

And what about the power button on the front of PC when you press it? Does it light up, what color, and is it steady or blinking?

You might want to watch Dell's video here and follow the instructions offered.

The Power Supply LED stays Off when you press the Power button.

The front Power button never lights up at all (or any other light for that matter).

The Dell video refers to a  Power Supply Diagnostic button that my system does not have.

Sounding like a failed PSU, but only connecting a known working PSU will answer the question.

You could try the paperclip test:

1. Power off and unplug
2. Press/hold power button for ~15 sec
3. Open case and disconnect main power connector that goes from PSU to motherboard
4. Using a bent paperclip, insert one end into a hole in the connector that goes to a green wire, and insert the other end of the paperclip into a hole that goes to a black wire. Do not cut or remove any wires from the connector.
5. Carefully/safely plug PC into working wall outlet

Fans and hard drive should spin up. If not, PSU is probably defective.

Caveats:

1. Only attempt the paperclip test if it's within your technical capabilities and can be done safely. There are youtube vids on the paperclip test if you need more instruction. Otherwise, take the PC to a reputable shop for diagnosis and repair
2. I can't guarantee a new PSU will fix the problem
3. Only you can decide how much $ to invest in this older system