Inspiron 560, 2 beeps, amber light flashing.

Sounds like incompatible RAM.  

If you reinstall the original RAM does it do it? 

Also what is the brand and type of new RAM you installed?

Dell's have a history of incompatibility with some memory.  No definite answer as one can work OK and in another not work.  However, Kingston Value Ram (KVR) seems to be problematic.   

The Dell spec's are:

1GB or 2GB memory modules.

1066Mhz DDR3

The Dell manual does not state what voltage the memory is, but a 3rd party site lists 1.5V.

You can try clearing BIOS to see if you can get it to recognize the new RAM. You may have to reinstall old RAM to do steps 1-2:

1. Reboot and immediately press F2 to open BIOS setup
2. Copy down all current BIOS settings
3. Power off, unplug
4. Press/hold power button for ~15 sec
5. Open case and remove motherboard battery (check Service Manual for details)
6. Press/hold power button for ~30 sec
7. Install new RAM in correct slots
8. Reinstall the battery (time for a fresh CR2032 3-volt coin cell battery?)
9. Close up and connect mouse, monitor and keyboard
10. Reboot

Dell validated Inspiron 560 Desktop memory with part number =

4 memory slots
Maximum 8GB

9V62Y 4GB, 1333MHz, 512x64, Unbuffered, DDR3, 240 pin, Dual Rank, 1.5v, Non-ECC
P223C 2GB, 1333MHz, 128x64, Unbuffered, DDR3, 240 pin, Dual Rank, 1.5v, Non-ECC
2CK3D 2GB, 1333MHz, 128x64, Unbuffered, DDR3, 240 pin, Dual Rank, 1.5v, Non-ECC
G8NT0 2GB, 1333MHz, 128x64, Unbuffered, DDR3, 240 pin, Single Rank, 1.5v, Non-ECC
1N7HK 2GB, 1333MHz, 128x64, Unbuffered, DDR3, 240 pin, Single Rank, 1.5v, Non-ECC
TW149 1GB, 1333MHz, 128x64, Unbuffered, DDR3, 240 pin, Dual Rank, 1.5v, Non-ECC
GR82X 1GB, 1333MHz, 128x64, Unbuffered, DDR3, 240 pin, Single Rank, 1.5v, Non-ECC

GKMX8 2GB, 1066MHz, 256X64, Unbuffered, DDR3, 240 pin, Dual Rank, 1.5v, Non-ECC
Y996D 2GB, 1066MHz, 256X64, Unbuffered, DDR3, 240 pin, Dual Rank, 1.5v, Non-ECC
F680F 1GB, 1066MHz, 128x64, Unbuffered, DDR3, 240 pin, Dual Rank, 1.5v, Non-ECC