Is wireless receiver + ethernet shield + 120x64 LCD too much for 1200mA power

In my central heating Arduino experiment I have a £10 wireless receiver, an ethernet shield and a 120x64 LCD all powered by 1200mA power 9 or 12v adapter. The ethernet shield and LCD seemed to be working fine but as soon as I added the wireless receiver to the project, it didn’t receive any messages. I took the LCD off and I started receiving my messages. What’s wrong here? Is it a simple case of requiring a better a power adapter? Or do I need to be beaten with a wet fish?

Did you make sure the voltage doesn't drop on any of the parts (LCD, etc)

Thanks! No I haven't/don't know what to do/need to be beaten with a wet fish. I am a noobie when it comes to electronics but fine on the programming side of things. I get the problem when as soon as I connect the LCD +5v in parallel with the receiver +5v, and I'm aware that the LCD and Ethernet shield are power hungry hence the need for a power supply.

You need to get a multimeter first. Even a cheap one ($10-20) on ebay would do. Then measure the current for each separate part.

I do have a multimeter, and all the devices are wired in parallel. If I put the multimeter in parrallel wouldn't that also read a drop of 5v too? I tried to measure current by putting the meter in series yesterday but got 0 amps :s