Hello,
Does the microphone have a battery-pack installed in it? If there is no dedicated battery in the Microphone (or it's wire), then it is not a self-powered Mic.
The port on the back of your iMac G5 is a Line-in port. It is not a Microphone port.
The operative word here is "Line"
A "Line" in port expects "Line-Level" audio.
Line-level audio is the level of audio you would find on the RCA jacks on your component stereo system's CD-Player, Tape Deck, etc.
Two devices commonly need pre-amplification. Those are Microphones and Record Players / Turn-Tables.
Neither of those devices provides a line-level audio signal. They both need to be pre-amplified first.
Pre-Amplified computer microphones are getting harder to find. But, they are available.
A pre-amplified microphone will have it's own power source (such as a set of AAA batteries). And, it will amplify the signal prior to sending it to the computer.
Don't make the mistake of purchasing a microphone that claims to be "amplified" and does not contain it's own power source. That is not the same thing. Rather it is a rather loose use of the term Amplified. I've seen lots of so-called "Amplified" Mic's that did not contain any form of booster at all.
Make sure you purchase one that has it's own power source (such as batteries).
Here is one example:
http://www.jr.com/JRProductPage.process?Product=24501
Now, if your Microphone does have a battery in it, and you still cannot hear yourself on the computer, go into the system preferences (Apple Menu --> System Preferences --> Sound), and select "Input". Then, adjust your input volume to see if that makes an improvement.
Also, check to see if your microphone has a volume knob on it to boost the signal strength. It probably doesn't. But, some powered Microphones will.
Or, if you want to use a regular Microphone like the the other one you have, you can purchase a "pre-amplifier". This is simply a small powered signal booster that plugs-in between your computer and the microphone. It will amplify the signal to "line-level" before sending it to the computer.
Unfortunately, pre-amplifiers can be rather expensive for small ones, and rather large for the cheaper ones.
If you are handy with electronics, here's a document on how to build your own pre-amp circuit:
http://www.epanorama.net/circuits/micamp.html
One external solution around $120 is this simple and compact pre-amp:
http://www.microphones.com/microphonegroup.cfm?URLID=Preamp-Series
There are several USB and FireWire solutions that are much cheaper.
Such as:
http://www.griffintechnology.com/products/imic/
But, they sometimes cause a bit of "latency" in your recording. Simply put, if you were singing along with something or needed your speech to be synchronized, then the USB or FireWire audio method might cause a noticeable delay in your recording.
If the only thing you are recording is your speech, then a bit of a delay in your recording probably would not be as noticeable.
The reason you can use a cheaper Microphone with a PC, is that it actually has both a Line-Level jack and a Microphone specific jack. Older Mac's such as the G3's had both as well. But, the newer Mac's just have the Line-Level jack.
Now, if you just want to use your existing Microphone, you could try using the Griffin iMic to make your current microphone work:
http://www.griffintechnology.com/products/imic/
It's about $40.
But, if you are wanting a simple and self-contained solution, then you might just go with a USB microphone.
Just keep in mind that you may have a bit of delay with a USB solution (either USB Mic or USB PreAmp) when you are speaking.
I have not used these, but here is a couple of USB Microphone solutions:
Microphone:
http://www.samsontech.com/products/productpage.cfm?prodID=1810
Head-set and Microphone:
http://www.macnn.com/reviews/review.php?id=199
Let me know if you have other questions.
I hope this helps.