it could be many things, but something to try first, before investing in hardware is the installation.
Did you install the OS on the current system or while it was in the other computer? An OS will not transfer systems as there are hardware/device settings saved.
The sounds are similar to ones i had when i built my first computer. Fans spin so the power supply is fine, if it beeps (assuming it can beep) then the motherboard is probably ok, when it stops the step after that it's doing a RAM and processor check, and one of them may be failing.