The PC should beep once the moment it's switched on. This is
true if you are using Award BIOS. One beep means it's working fine,
and everything would load as per normal.
If the moment you switch on you hear numerous beeps and nothing on
screen, it indicates hardware problems. RAM, external cards, hard
disks and CD/DVD drives are the causes.
If it loads halfway then beeps, most likely your keyboard is not
connected, and it would no keyboard is detected error.
If it beeps no matter what change, it has probably got to do with
the new PSU. If your motherboard is old, it can't take the high
power usage of the new PSU. Also, most older motherboards use 24
pins for the PSU. If you get one with lesser than 24 pins and
connected wrongly, it will beep.
For hard disk and CD/DVD drives, especially new ones, use cable
select if possible. If you set master or slave settings manually,
please make sure that they are done correctly. Otherwise, it will
mess up everything.
Again, this could be new PSU. Make sure your motherboard can
take it if it is rather old. If your new PSU uses less than 24
pins, make sure it is plugged in correctly. Change the BIOS
settings to boot from hard disk once Windows is installed.