Doesn't seem to me like your CPU or PSU is the problem.
Once the computer is on try this:
Press Windows Key + R
Type: msconfig
Press enter
Go to the Startup Tab.
Disable as much as you can.
Reboot
This could improve your boot speed quite well.
If it doesn't, I would recommend backing up your data, and formatting your computer.
250W is quite low though. I would upgrade the PSU regardless.