Monitors are not wireless devices. What model of Westinghouse monitor is it? I can check my stack of manuals for a specific location for the power button.
General setup for connecting a monitor to a computer:
With the computer and the monitor off, first make sure that the monitor power and data cables (VGA for example) are securely connected to the monitor. Plug the data cable into the corresponding port on the back of the computer. Make sure to use the active video port (if you have a video card, use those ports and not the ones on the motherboard). Plug the power cable into a good electrical outlet. Turn on the monitor with the power button on the lower right hand side of the monitor as you look at the front of the unit (I'm using the LTV-19W3 for one possible location of the power button). (Some other monitors will have the power button on the top or under the bezel at the front of the unit.). If the monitor has several source options, press the Input or Source button to set the monitor to the one that matches the cable currently in use.
Now turn on the computer. (Please note that if the monitor is turned on after the computer, the computer may not properly identify the resolution. You should see something on the screen, even if it is a No Signal message.) Do you get an image on the screen? (I've found on some new computers with multiple video ports available, only one is active when the computer is delivered. You have to use a monitor with the cable for the active port to switch to another port (and changing cables).)
Next thing is to check if the monitor is good. Did a light come on indicating that the monitor had power (or was in standby)? If there is no power indications, then the power supply or the power cord has failed (try another power cord - listed as a CPU/monitor power cord at most shops). Then try a new data cable. Check if the monitor works on another computer if you can. The next items that can fail are the backlights, backlight inverter or video board itself.
It's probably a backlight or backlight inverter issue if the problem occurs on all sources and the onscreen menus. (The backlight itself usually fades or makes the on-screen image change to pink/red.) With a bad backlight, you'll usually see a very dim image if you look at the monitor from an inch from the screen. Block the room light from overwhelming this image (sometimes a carefully positioned flashlight will help you see something). If the inverter or video board is bad, you will see nothing. For an out-of-warranty monitor, open up the back of the monitor and remove the shielding. Look for any scorch marks or bulging or damaged capacitors. (Sometimes other parts will fail on this part but these can be spotted easily. Capacitors look like cylinders on a tripod.) The scorch mark and smoke may indicate a resistor or zener diode that had been used as a fuse and is now gone.
If you borrow (or have a) high-end multimeter (able to measure high frequencies - 50 kHz) or an oscilloscope, hold the multimeter probes a fraction of an inch apart about an inch above the inverter board and power up the TV. If you see a 1 or an actual value, you have a good inverter. If you see a reading near 0, the board is bad or the multimeter can't resolve the frequency.
In either case, you can buy a replacement inverter for $50-150 and just do a simple swap. Disconnect all of the wires (connections are similar to molex and ribbon cables in a computer) and remove board (a few screws usually). Connect the cables to the new inverter. (If you google backlight inverter replacement, you'll find videos and text descriptions.) Note the part number on the board, including the Rev number, and order the exact one (shopjimmy.com or lcdparts.net are good starting points). Universal inverters do exist but can result in reversed controls (up to lower the brightness). Replacing individual parts on the board is cheaper but more prone to not tracking down all of the bad parts.
If the inverter is good, then it's probably backlights themselves (several in most monitors). These are sandwiched on the perimeter of the monitor (usually under some tape that holds the lamp, reflector and other parts together. You need to order by length and width and get ones for your monitor size. Separate the panel from the bezel. Remove the tape, and separate the reflector (make a note of how things are put together) then you have to Dremel (or use another rotary tool) to remove the plastic to get the backlight out. (They are often molded into the frame.) Then put in the new backlight and reassemble everything. See http://www.lcdparts.net/howto/default.aspx
for more information but for an overview: http://www.inventgeek.com/Projects/BacklightFix/overview.aspx
. Then push the new backlights into place, reconnect the wires and close up the sandwich of tape and other parts around the screen. Then replace it in the bezel.
With a good spare backlight, you can test an inverter for condition (plug together and turn on the tv while the box is open). Similarly a good inverter can test the backlight.
I hope this helps.
(since the monitor is 4 years old, I'm not sure it's worth fixing when LED-backlit 19" widescreen 1600x900 resolution monitors are currently being sold for $100.)