You haven't mentioned which version of AE you are using. It's possible that AE is running under Rosetta emulation on your G5, which will slow it considerably. If possible, upgrade to a newer computer with faster Intel processors.
However, the primary problem you have is lack of RAM. Your 1GB doesn't even meet the recommended minimum specs required for AE CS4 (2GB), and the fact that you're working with a quite hi-res comp (3476 x 2494) with plenty of layers (up to 600) means that AE will be paging loads of data to your hard drive in order to cope. (Frankly, I'm surprised it's managing to do as well as it has!)
Get more RAM, at LEAST 4 GB for this kind of work.
Depending on your hardware and AE version (and how much extra RAM you can install) you may be able to use multi-processor rendering. You need around 2GB of RAM for each processor core in your system to work efficiently. Don't even consider multi-processsor rendering with your current amount of RAM.
The quality of your video card is irrelevant to the software renderer in AE.
DPI is also irrelevant in video applications. The question is, what resolution are your PSDs - ie pixels wide and high? An image that's 500 pixels x 500 pixels uses one quarter of the RAM required by an image that's 1000 x 1000 pixels. They bigger they are, the more RAM they require to be processed.
Yes, changing resolution of source material after creating your AE animation may have serious consequences within AE, particularly with effects like the Puppet tool.
As Andrew mentioned, 1GB RAM is very little for such a large composition.
Also, one minute per frame is not unheard of for the final render of a large, complex composition.
For a list of tips on how to improve performance, see "Improve performance".
Yupp, as the others said, 1GB is simply not good enough. What actually happens is that AE is constantly loading and unloading data from memory and that part is slowing down things. In fact the shuffling around of the data might increase per-frame rendering time to multiples of what it would take without it. RAM for such old computers as yours should be dirt cheap, so you should really consider shelving out those 30 bucks in your favorite electronics store, assuming you want to hang on to your G5 and not buy a new machine.
Mylenium, Todd, Andrew, Thank you for your answers! I am ordering 4 GB of ram tonight.
I have AE CS3, and unfortunately I am not in a situation where I could buy a new computer, but I am sure that +4 GB will help a lot.
Since I posted this thread I also realised that my system hard drive was really full (only 9 GB left), so I mad a huge cleaning and back up, so I have now 50 GB free.