Unexpected shutdown the computer keeps on shutting down and we can't even work even just a few minutes and this just happened last month and still continuing until today

It sounds like you are experiencing an issue with your Dell OptiPlex 780 computer where it is shutting down unexpectedly. There are a few potential causes for this issue, and several potential solutions that you can try to resolve it.
Here are a few steps you can try:

1. Check for updates: Make sure that your computer is up to date with the latest Windows updates. Sometimes, these updates can fix issues with the operating system that may be causing your computer to shut down unexpectedly.
2. Check for hardware issues: Make sure that all of your computer's hardware is properly installed and functioning correctly. If you have recently installed any new hardware, it's possible that it could be causing the issue.
3. Check for malware: Run a malware scan to make sure that your computer is not infected with any malicious software. If you find any malware, remove it as it could be causing the shutdown issue.
4. Check for overheating: Make sure that your computer's internal temperature is not too high. If it is, it could be causing the shutdown issue. You can try cleaning the inside of your computer and making sure that the air vents are not blocked to help keep the temperature down.
5. Check the power supply: Make sure that your computer is receiving a stable power supply. If it's not, it could be causing the shutdown issue.

If none of these steps help to resolve the issue, you may want to try contacting Dell for further assistance. They may be able to help you diagnose and fix the problem.

If AC adapter is connected and the system gets shutdown automatically it is for sure that this problem is not for battery. You can try going to properties of My computer - Advance system setting - startup and recovery settings - automatically restart

try using a cooler pad for your laptop for heating issue,
try changing the RAM also sometimes the faulty RAM also does this

I usually try to hold the power button for >5 seconds to reset it. No lights even when plugged in?

have you tried to hold the power button down for 5 seconds? if that doesn't work, it's possible that when you click the shut down the last option used was the hibernate option. when you click the orb click the arrow pointing to the right next to the power indicator and make sure it's set to shut down and not hibernate

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Running intense program with the lid closed will cause a sharp rise in temperature making the laptop hotter than it should be leading it into a shutdown. The second issue, windows should be shutdown properly rather than closing the lid, this makes the operational system unstable and will cause files to corrupt eventually.

It's shutting down automatically due to heat peaking. You need to turn off until you are ready to use it.

Two things you can do, you can hold down the power button, keeping it held down, should power it off. The other solution is to remove the battery, this should cause the Notebook to power down

If the Computer restarts randomly, then the issue might be due to any damaged Operating System Files.
But, if the Computer shuts down randomly, it is due to the Processor.
All the Processors will be designed in such a way that, if there is any overheating issues, the Computer will shut down randomly.
The overheating might occur due to the malfunction of the Cooling Fan in the Computer.
As this is a overheating issue, it would be better to get the Unit examined at the Service Center.
Replacing the Cooling Fan in the Computer should resolve the issue.

It might be a thermal shutdown. If the computer is more than 6 months old, this is what I expect it to be. Try leaving your case's side panel open after checking for dust buildup.

Alternatively, it might be simply unstable. This usually doesn't happen for prebuilt machines, but it can happen. While the computer is booting, enter the BIOS (Basic Input Output System) by pressing the button at the first screen you see. It should say ''Press X button to enter BIOS''. The button is usually Delete, but can be something else like F12. Once you are in the BIOS, choose the option that suggests a return to default settings. This will let the PC automatically bring back all settings to what they should be and usually makes sure it's not unstable.

Lastly, it can be a software problem. Try booting into Safe Mode instead and see how long the PC stays on. If it stays on indefinitely then it is a virus or software problem. Either put an anti-virus program on a USB key and quickly have it scan for problems, or reinstall the operating system to fix a possible bug.