Perhaps it could also be a behavior of CRT monitor with tube life expired. May be PC is ready but monitor doesn't show up immediately. try with another monitor for test purpose.
Next possibility, is low RAM and maximum files loaded, and some anti-virus package even.After the machine comes to life, you may check the capacity of RAM, and increase if the machine is proposed to be used for some more years.
You may remove most files at start up. Uninstall the anti-virus for the time being.
I really dont understand the relevance of PSU in booting delay.