I own a Macintosh eMac G4 that runs on Mac OS X Panther (10.3.9) from 2004? or 2005? Anyways, when I push the power button, I hear some startup sounds, but then it's goes silent with a weird beeping sound three times. There is nothing on the screen, it's just black, like when it's a Sleep Mode, but it's not sleeping or responding to mouse gestures or random keyboards buttons and shortcuts. What is wrong with my computer? Is it dead hard drive? Is the memory to full for startup? Is it computer decay and after some odd years it ceases to operate? Please help!

I've used legacy Macs for years, and this sounds like a memory problem to me.
All G4 Macs (eMac is one) have a POST (Power Up Self Test) mode. When you switch on the Mac, it takes itself through a self test of its hardware.
If it finds a problem it halts the bootup sequence to ensure no damage is done. This happens before the Mac Chime.
The Mac will beep a number of times if it finds an issue.
No beeps will mean everything is ok and your mac will boot up (this is the normal day to day switch on switch off usage we expect from a mac).
As you have a later emac, these are a breakdown of the beeps and what they mean.

1 Beep: The computer has found no RAM installed. Or it thinks it hasn't. If your mac was working fine yesterday, and you haven't dropped it or poured beer into the slots, have a look at the advice I give for 3 beeps, this should be done before you think about contacting a Mac Guy.

2 Beeps: You have Ram modules fitted that are incompatible with each other. This can be proved by removing one Ram module and rebooting. It should start up ok. Check what is written on both Ram modules and ensure they match. If not, buy another so you have a matching pair and refit. Mac should the work fine.

3 Beeps: The eMac is telling you that both banks of Ram are faulty. Go to Youtube and search for changing RAM on an emac.
There are lots of vids there that will show you how easy it is to change the ram. Simply open up the memory bay, take out the ram, and reseat both modules. Restart.
Works ok? You just needed to reseat your memory modules. Everything is ok.

Didn't work? Here's the logical faultfind to test everything. I'll use DW for didnt work and W for worked depending on the results you get.

Take out both modules. Insert one module in one slot and restart.

W? You have just proved that RAM module and slot works ok. Even if nothing else works below, at least your mac will work on reduced memory.

DW? Put the other RAM module in that same slot and restart.

W? Both Ram modules are fine, and you have a problem with that second slot.

DW? I Suspect that Ram chip that you've just put in is faulty.
Test this by putting the RAM module you know is working into that second slot. Restart.

If it fires up it definitely proves the ram module has gone kerplung. You just need to buy a ram chip that mirrors the working one (i.e. the same terminology on the label). You can find these on ebay for small bucks. Make sure they are the same, (if they aren't that's why you get 2 beeps).

4 Beeps: No boot images in the boot ROM/bad system configuration block. Apple or good Pc dealer needs to have input.

5 Beeps: Get scared and reach for your wallet. Your eMac processor has failed completely.

Also some macs will flash their LED at the same time for the same amount as the beeps (plus one). The beeps activate only once on startup, but the LED's will continue until it's shut down.

Hope this is'nt too geeky, and has helped. I've used legacy Macs for years, and this sounds like a memory problem to me. All G4 Macs (eMac is one) have a POST (Power Up Self Test) mode. When you switch on the Mac, it takes itself through a self test of its hardware. If it finds a problem it halts the bootup sequence to ensure no damage is done. This happens before the Mac Chime. The Mac will beep a number of times if it finds an issue. No beeps will mean everything is ok and your mac will boot up (this is the normal day to day switch on switch off usage we expect from a mac). As you have a later emac, these are a breakdown of the beeps and what they mean. 1 Beep: The computer has found no RAM installed. Or it thinks it hasn't. If your mac was working fine yesterday, and you haven't dropped it or poured beer into the slots, have a look at the advice I give for 3 beeps, this should be done before you think about contacting a Mac Guy. 2 Beeps: You have Ram modules fitted that are incompatible with each other. This can be proved by removing one Ram module and rebooting. It should start up ok. Check what is written on both Ram modules and ensure they match. If not, buy another so you have a matching pair and refit. Mac should the work fine. 3 Beeps: The eMac is telling you that both banks of Ram are faulty. Go to Youtube and search for changing RAM on an emac. There are lots of vids there that will show you how easy it is to change the ram. Simply open up the memory bay, take out the ram, and reseat both modules. Restart. Works ok? You just needed to reseat your memory modules. Everything is ok. Didn't work? Here's the logical faultfind to test everything. I'll use DW for didnt work and W for worked depending on the results you get. Take out both modules. Insert one module in one slot and restart. W? You have just proved that RAM module and slot works ok. Even if nothing else works below, at least your mac will work on reduced memory. DW? Put the other RAM module in that same slot and restart. W? Both Ram modules are fine, and you have a problem with that second slot. DW? I Suspect that Ram chip that you've just put in is faulty. Test this by putting the RAM module you know is working into that second slot. Restart. If it fires up it definitely proves the ram module has gone kerplung. You just need to buy a ram chip that mirrors the working one (i.e. the same terminology on the label). You can find these on ebay for small bucks. Make sure they are the same, (if they aren't that's why you get 2 beeps). 4 Beeps: No boot images in the boot ROM/bad system configuration block. Apple or good Pc dealer needs to have input. 5 Beeps: Get scared and reach for your wallet. Your eMac processor has failed completely. Also some macs will flash their LED at the same time for the same amount as the beeps (plus one). The beeps activate only once on startup, but the LED's will continue until it's shut down. Hope this is'nt too geeky, and has helped.