Hi,
It can depend on where you are located and the problem found with the notebook, so check with your local service center or store to get the details, or click on this
link for the contact information on the ASUS website.
Yes, depending on your situation and the problem found, you may prefer to save your money for a newer notebook under warranty rather than spending too much on an older out-of-warranty unit.
The problem could be caused by different things including the motherboard, video card, memory, and more.
1. Make sure you are still using the original AC adapter or a known working AC adapter, but if you are careful about the metal battery contacts in the notebook, you can run the notebook without the battery just to eliminate the possibility of a very bad battery (not a common problem, but easy enough to try?).
2. If you can safely remove any extra memory modules (check page 16 and 17 of the user manual for more details), you may want to try them one at a time to see if any memory sticks could be bad (or just have dirty contacts?) although it may not be a common memory issue that the unit doesn't power on at all.
3. It rarely helps and may not be worth trying, but according to page 17 of the posted English G73Jh user manual 1229-b, your notebook has an emergency shutdown button. If you are comfortable trying it, remove the battery and unplug the adapter (no Power to the notebook) to push this button a couple times with a straightened paper clip and plug back the AC power (without battery) to try to power on again.
Newer ASUS notebook models don't have the shutdown/reset button anymore if anybody is wondering.
You should have a copy of the user manual under your C: drive (ASUS or eSupport folder?), but you can also download it
here through the 'downloads' tab.
Good luck!