My ACER ASPIRE 5734Z is not responding after depressing the power on button. It only indicates when the power cord is plugged
A power reset, holding the power button for 10 to 30 seconds with the battery out and charger unplugged, can help to push out the extra power that may be held within the motherboard and other parts of the computer that can stop a computer from powering on. However, it does not always work, or at least the first couple times trying to perform the power reset.
I would try the above first, then try using another battery if possible, and then try another charger should the other suggestions fail. I have to ask, does the power led stay on when plugged in or does the light flash in a certain pattern? If the light flashes, count how many times it does flash per cycle (there should be a pause before the flashing starts again). Depending on the flash sequence, it could mean anything from a bad power input (the part you plug the charger into as it can become damaged) to a bad motherboard.
Also, do you hear the CPU fan or anything else power up when you try to start the computer? Any extra information you can give can help us figure out possible causes and suggestions you can perform. At best, you only need to perform a power reset, replace the battery, ore replace the charger. At worst, the motherboard is bad and you would need to replace it (usually not worth doing since it costs almost as much as purchasing a new computer), or buy a new computer.
Many laptops won't power on if the battery is removed, or if the battery has failed. Buy a replacement battery or have yours tested to see if it's good.
Some laptop power supplies (power bricks) have fuses which will cut the power if they're blown; it's not impossible for it to supply enough power to turn on the "charge" LED if the power supply has more than one power output (for example, 5V + 12V) - the laptop won't power on without both outputs, but only one turns on the LED. Try having the power supply tested, or use another.
@Hovsep A: Most laptop CMOS batteries are buried somewhere under a bottom panel, making them difficult to replace (especially on older systems), and I've yet to see a bad CMOS battery that made a system fail to start in my 20 years' working on PCs. More likely it will reset the clock and system settings instead.
@Hovsep A: From that article: "...but should the computer not receive power, whether it be from an electrical source or a battery source, all information stored on the computer and not backed up elsewhere can be lost." Right. Unplugging the computer or removing the CMOS battery will erase the hard drive. Sounds like someone doesn't know what they're talking about, or over-simplifying.
reset cmos battery
Remove the battery and unplug the laptop. Press the power button for 10 seconds and let go. Now plug in the power supply and try switching it on. If it still fails to start up, there's a hardware problem.
If it does work, switch it off, plug the battery back in and try it again. If it works, great! If it doesn't, there's a problem witih the battery.
I have done this but still not responding
Press and hold the power button for at least 5 seconds. Release it, then press it again.