Dell demension 4600 wont turn on

SOURCE: No power to Dell demension 5100 desktop

If there is no activity whatsoever when you press the power button on than you have likely blown the internal power supply fuse. This will need a technician to repair.

SOURCE: I have a Dell Dimension 4600 and it won't boot up.

i would have to disagree with jerry, while that seems reasonable if the motherboard fan isn't running at all then whether or not the video card is ok is somewhat irrelevant.
I would agree somewhat though, i think the PSU might be a good thing to check to see if it is functional.
when you power it on does the CPU fan start or shudder at least ? that would be my first guess for a problem if you had been having any problems recently

SOURCE: Computer will not turn on

• Blinking Amber/yellow: Initial state of LED at power up.
  Indicates system has power, but the POWER_GOOD signal is not yet active.
  If the hard drive LED is off, it is probable that the power supply needs to be replaced.
  If the hard drive LED is on, it is probable that an onboard regulator or VRM has failed.

SOURCE: Front Panel help for Dell Dimension 4600

Most Dell's have a connector that all of the front panel wires go in to. That connector should only fit one place on your motherboard. If you use a flashlight you may be able to see some writing on the motherboard that will lead you to where it goes.

SOURCE: Have a dell dimension 4600. I have a blinking

The two biggest culprits would be:

the power supply and the motherboard.

I'd start with the power supply since it's cheap and easy to install.

Find a local computer shop that sells 'em.

Make sure they've got a 100% return policy.

Swap 'em, if it works problem solved.

If not it's probably the motherboard. You could always have a local tech check it out.

Make sure they provide FREE diagnostics. It shouldn't cost you anything to have ti looked at.