Hello and welcome to Bleeping Computer.
You did not post the model number of your computer so that makes it difficult to offer any suggestions that are related to your specific hardware.
It also makes it difficult to determine the exact age of your computer system and how badly the case could be possibly a victim of dust related accumulation.
Please open the computer case and examine your hardware for signs of dust clogged up cooling fans.
The PSU might be tougher to examine, but you should still be able to see the condition of the cooling fans without opening the PSU and I recommend that you DO NOT open the PSU as there is components inside that case that can cause electrical shock or severe electrical burns to fingers!
There is no doubt, that your system has a failed component, however, that does not mean your system is trash. Most PSU (Power Supply) have a fuse on the primary side of the transformer. Sometimes, this fuse blows before the unit is severely damaged. The problem with this fuse, is that it is not easy to replace because it is located inside the PSU case and requires opening it to gain access to the fuse.
If your computer did over heat because of dust clogs embedded in any cooling fans, I would first disconnect the computer from the mains (AC power line) and at least try to clean out the dust and then inspect the motherboard and the power connectors for signs of a dark brown or black (charred) appearance. I recommend touching the computer case for a few seconds before touching the parts inside the computer case to help prevent possible damage from static electrical discharge. There is a possibility the area is burned to the point the connection has failed and can no longer be of any use in the safe operation of the computer system.
As for the PSU, you could have someone who understands the dangers involved with working with stored AC voltage check the status of the fuse and the condition of the PSU's components, such as are there any burned or browned circuit board areas. If not, you could try a PSU replacement and see if the computer powers back up again.
I truly--without looking at the computer in person--can not say if your motherboard is fried or not, but that is also a possibility.
Inspection is key to our next course of action here and I recommend that you do such an inspection and post back any obvious conditions you observe.