The CPU is located in that corner, and it could be having a heat issue. There is a fan in that corner which is to keep the CPU's temperature down, if it is not working then the CPU will heat up quickly and could cause the computer to not start. Another possibility could be that the fan is full of dust. This
site has instructions on how to open the access to the CPU and fan from the bottom, open this access and inspect the fan. If the fan is full of dust try blowing it out with a can of air like Duster, you can get this at any shop that sells computer parts, or even some hardware stores.
If you do open the case, be aware that your body can have a static electricity charge built up, you need to discharge yourself to something close at hand that is grounded . Electrical static discharges can kill the CPU or any other chip in the computer.