Computer won't start

Lets start here so others can assist.

Does it make any beeping sounds?
Anything come up on the screen?

Power supply failing might not have enough power for everything any more.
Saw the 4 pin connector going to the motherboard did not see the 12 pin power connection.

Motherboard failing

What are the system specs
Make and models
Age of parts in the system approx is ok

Events leading up to

Make and model of the power supply
Operating system Version Build and Desktop Environment
Processor
RAM

Bocki said:

The Computer itself is about 10 years old, but was repaired in 2015.

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What was repaired.

Could be the power supply giving out.
Could be the thermal paste needs replaced.
Could be the display card.
Could be the motherboard.

Is there onboard graphic's? Depending on you CPU that may work.

Bocki said:

The Mainboard was swapped for a New one

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If the MB was a straight swap it should have an onboard BIOS error speaker.

Remove both sticks of RAM from the MB, hook up to the power and press the case power button, let us know if you get any error beeps.

Do you have a different PSU that you can try that is the same or more wattage?

You have traced all the cables and made sure that they are not loose. Try reseating them and see if that helps.

The power button (power indicator) what color is it does it flash and in what pattern?

Bocki said:

Already tried it. Both for ram and the graohics card i get the corresponding beeps.

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Anything that you had already tried should have been mentioned in your OP.

Getting error beeps with the RAM removed normally suggests that the MB and RAM are ok and that the problem is with an item of hardware that gets checked after the MB and RAM as part of the power on self test (POST) the next thing that gets checked is the graphics solution and being that you are getting no display your add on GPU is implicated one way or another.

Bocki said:

After reseating the ram and graphics card i got it to post and boot, and was able to "log in". When a programm started it crashed

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Can you describe what actually happened for us.

Software such as Windows can crash and when it does crash you get a BSOD and when enabled a crash dmp is generated.

Hardware failure such as a weak power supply and/or overheating are not software related and when a computer freezes, suddenly turns off or the screen goes jumbled the behaviour should be described as the "computer shut down unexpectedly" etc and not as having crashed as the latter implies a software issue as opposed to an obvious hardware issue when described properly.

Having the correct info means that helpers will not be looking for a software issue when the problem is clearly hardware related.

Thread closed due to lack of feedback from the OP.