You are running Windows XP on a T5026 Emachine. It won't re boot using some steps as provided on a black screen. You tried turning off your computer and disconnecting all components.
When rebooting, a screen saying that Windows did not start comes up. You tried rebooting in safe mode, last known good configuration mode, etc. When trying either of those modes, you get a count down for thirty seconds and it starts all over again.
If you can't boot into any of the safe mode options then do you have a Windows XP installation disc available? If you do then you can boot off that CD and go into recovery console. Type in "chkdsk /f /r" into that console.
Also, you can type in "sfc /scannow" into that recovery console. Both those scans might fix your issue. If you don't have a Windows installation disc, please power on that computer and immediately start tapping an F11 key until a recovery partition options menu opens.
See if there is a repair option. Otherwise you can try a factory recovery to restore that computer back to the way it was when you bought it. There might be an option to back up your data before restoring it or restoring Windows XP to a previous state.
If your computer does not utilize an F11 key for a repair or recovery option, then try to perform a google search for your computer make and model number or consult your computer manual to obtain correct key stroke.