Don't hold the power button while connecting the charger. The laptop can get into a weird mode.
If the battery is disconnected, sometimes you may need to press the power button several times or perhaps may even need to hold the power button for a second or two in order to power on the laptop. Sometimes just wait a few minutes after connecting the charger before attempting to power on the laptop.
Try an SMC Reset by holding down the following keys on the built-in keyboard:
Left Shift + Left Control + Left Option keys. Then while still holding these three keys press the power button.
Keep an eye on the Magsafe LED to see whether it goes out for a second before lighting again which would indicate a successful SMC Reset. I realize Apple's current instructions for an SMC Reset may not mention this method for a 2008 model, but I am sure I was using this key combination on them. It does not hurt to try.
If this does not work, then you likely have some sort of hardware problem with the laptop. Most likely the Logic Board is bad, but there is a slim possibility the DC-In Board is bad, or perhaps another internal component is bad. You can disconnect everything from the Logic Board (Display, Keyboard, Trackpad, I/O Board, Hard drive & Optical drive cables) except for the DC-In Board to see whether the laptop will power on. There are special pads on the Logic Board which can be used to power on the laptop when the keyboard is disconnected. I would even remove both memory modules as well. If the laptop does not power on, then it means the Logic Board or DC-In Board is bad (most likely the Logic Board).
https://beetstech.com/blog/where-are-macbook-pro-unibody-power-on-pads-located
