Why does it work only when connected to power supply?

it appears the power supply is faulty, as with a high electrical resistance in line with the load. My guess is carbon build.
Power supplies or sources have internal resistance and can not deliver more amperes than rated at. In your case there would be a resistance that allows you to read voltage with no load connected, actualy the only load would be your voltage meter, 10 mega ohms per volt? Try using a solenoid type voltage dsetector and you'd get no volts detected, because there is a high resistance either in the wiring or power source.
Trouble shoot: disconnect the wiring from the power source, short out the wires at the load, with the load disconnected, read ohms on the wires or conductor where they were disconnected from the source, it should be close to a few ohms but not high ohms, if your wires check out ok, then go to the power supply, is there a circuit breaker or electric connection offering high ohmage to the circuit? A load can be connected here to the source, a head lamp or something hungry for power but don't exceed or overload the power source.
Yes, this is about voltage drop in series with the load, loosing all your voltage in a high resistance in line with the circuit, not across the line but in line, in series.

most if not all systems require a power source directly linked to the batterys main supply. depending on how your system is installed, you may also have it connected to a Switched Power Source, such as your car radio, that will only turn on when the ignition is switched to on. if im understanding your dilemma correctly, and the light stays on and such - possibly wire the system differently with a switched power source that will disconnect whenever you choose

is this the only input where the TV does this? what happens when you disconnect this source? May be your source.

If the TV does this no matter what input, perhaps you have some leaky caps on the power supply PCB,. These can usually be detected by their bulging tops & usually self replaced (if you have the wherewithall) at a cost of less than $10.00

CONTINUAL DISCONNECTION OF WIRELESS CONNECTION
There are a few things that can cause you to lose wireless connection with your wireless router. 1. Weak signal strength, check the signal strength on your wireless card. If it is weak move the wireless router away from brick or concrete walls and if possible locate the wireless router higher up. 2. Have you secured your wireless router from people near your from unauthorized access? i.e. change the default password, setup encryption use WPA2 or WPA, change the default SSID, and turn off SSID broadcast, and for added protection, enable MAC address filtering which allows only the MAC address/es of your wireless card/s to connect to your wireless router. 3. You could be getting interference from electrical sources such as air conditioners, arc welders, washing machines etc. If so, the power supply to the wireless routers and computers etc should be connected to a surge protection power board, better still connect your computer equipment to an UPS (Uninterrupted Power Supply). 4. Check the channels of the wireless routers and access points in your area and change the broadcast channel on your wireless router to an unused channel or one that is currently used but has the weakest signal strength. This will minimize interference with your wireless router from other wireless routers and access points in your area.

Some power supplies have a short circuit protection. it turn off the power supply if it detect an overload/short condition.

Theres no specific order for power supply wires. Just make sure it is disconnected from a power source and connect the Motherboard and optical drive cables to their respective plugs(plugs are standard for most motherboards).

Hello,
What sources do you have connected to the receiver? The thing to do is to disconnect your sources one at a time and see if one of those eliminates that hum.

This would seem like the power supply is broken and the computer is working off the battery or the setting need to be changed in power management. Whenever you disconnect the power supply and work form the battery, as power saving mode, windows will dim the back light to the display. First check if the power supply is charging the battery and then check your settings in the following: Start menu -  Programs - IBM - Battery MaxiMiser Wizard. Follow the steps until you get to the LDC display level. You may need to increase that.

I had the same problem with my dlink (not wireless). Try going to their website and configure the router. It worked to me.