The PowerMac G5 can't start up correctly with only one stick of memory. If you look at the slots (there are 8 slots), you will see two separate sticks, or 4, 6, or 8 as you fill up those slots.
The standard shipping configuration for your 2.7 dual, is 512MB - 2 x 256 MB sticks. You may have 1 GB - and with one 512, you have another 512 in its paired slot. If you can read the label of one stick of memory, and it says 512MB, then you should reset the other 512MB stick in its other slot. - There must be a second stick - your G5 won't work without it.
After doing that, check your System Profiler, memory tab, to see what that says about your installed memory, and which slots are in use.
You can add DIMMs, provided they are installed in pairs of equal size, one per bank, from the center outward. A diagram marked on the logic board near the DIMM slots illustrates how the pairs must be installed.