I have a Dell Inspiron 546 running Windows Vista. When turning it on the Start button lights up, but the display very quickly goes into power saving mode. Nothing further can be done. The computer or display will not respond.

Well as per your recent comments, it seemed you've already tried removing the CMOS battery. There are many possible causes, like the Video card, the Ram, the Bios, the Reset switch, the front panel connector or even the hard disk drive or the CD/DVD drive or Power Supply unit.

First, you need to disconnect or uninstall everything from the motherboard except the Processor with HeatSink Fan and the Power Connector(s). Unplug the Front Panel connectors (the connectors which come out from the front part of the cabinet, connected to the motherboard). You need to be careful with the main Panel, i.e. the power switch, reset switch, hddled, power led. Before you unplug them, note down the connection sequence if you might forget it. Also take note of the power switch pins, you'll need to short it after a while. Unplug the HDD data and power cables, Cd/Dvd Drive's cables, and everything else. Remove the ram, remove the bios battery.
(don't remove/disconnect the system speaker)
Now, connect the power cord and the monitor on the back, power on the monitor (I would recommend you to connect the monitor via VGA), take a screw driver and short the power switch pin on the motherboard (I've mentioned this to you to take note). Look at the cpu fan and on the monitor, at least the system speaker should beep this time with the beep codes indicating that there's no Ram/Memory installed. (If nothing happens, then there's problem with the motherboard, could be the video card or could be the bios or something else) If so, then turn off and install one Ram. Again power up and check the status, if there's nothing wrong with the Ram, Motherboard, Bios or video Card, then you must see the Bios' System info screen (black screen with white texts after the Dell Logo flashes). If it doesn't seem anything happen, then try with the other/another ram. (If it fails, then there's problem on the motherboard, you better get another than repairing it.)

If it boots up with the Bios System info screen, then turn off and connect the front panel and other panels, like usb or audio etc.. Again power On the machine from the Power switch (this time On/Off switch), verify what happens. if it's ok, turn off and reconnect the hdd and the dvd drive and so on.... untill everything is reconnected and reinstalled or you'll stuck somewhere during the steps when the faulty component is installed.
Let me know the outcome, sorry, this is too long.....but I don't want you to get confused.

Hi. Were you able to see the the DELL post screen when you turn on the computer? Take out the battery and unplugged the power adapter from your computer and to the wall socket. Press and hold the power button for 30 secs. Put everything back in then turn on the computer.