Before strt-up, black screen appears with white font message saying: "problem detected: a fan is not working properly. To avoid further damage or losing data the computer will shut down in 15 seconds" Unless I press enter within 15 seconds, it will shut down. If I press enter and continue to log in to the main screen, it will only take a matter of 10-15 minutes before the computer will heat up
You need to replace the fan that isn't spinning.
The obvious answer is to replace the faulty fan. If the main cooling fan is not working of course it will heat up. This is most likely the fan on the CPU heat-sink. Assuming it is a desktop, replacing the heat sink fan is a fairly simple operation. If it is a laptop, it is a bit more difficult.
Knowing the model number of the computer in question would help.
Stuart
Is this a desktop PC? You need to open it up and take a look. The fan causing the problem may be obvious.
Seriously? The message is clear. You need to fix the fan issue.