You can put an extra power supply near your computer, and remove just the plugs from the built in power supply, then place the plugs for the outside computer in those locations, and see if that helps.
You don't leave it like this. This is only a troubleshooting method to see if another power supply resolves the issue.
If you don't know what to do, or are afraid, then don't do this. Find a competent person who knows what s/he is doing.
You need to find a power supply that has AT LEAST the power rating of the inside one, which may be bad.
You need to find a power supply that has all the needed plugs that are needed. Power supplies have evolved, as some new connections are needed in today's computers, those new connectors have been added. If you find a that your replacement power supply has more plugs than you need, that should be OK, even if unused.
And re-read that Caution shown above.
I'm having problems with my computer. One day, it worked fine, the next, it stopped working. The only other thing happening with the computer during this time is that the wireless keyboard also stopped working. This happened before the computer stopped working. The wireless mouse continued to work so the computer was usable. The keyboard was removed to be replaced. Another day, I tried to power on the computer to check something, and then it wouldn't power on. We now have a new keyboard, but the computer won't turn on.
When the button is pushed, an orange light flashes. It stops flashing when the power button is no longer being pushed. No sound/fan comes from the computer while this happens. The computer seems to make no effort to turn on.
I have a Dell Optiplex GX620.