Xynther,
We will be honest when we tell you attempting to fix a laptop is going to be extremely difficult for an end-user. However to answer your question, commonly when troubleshooting power issues you first of course look at the power plug. Make sure if the power AC power plug has a LED that it is on indicating power and feel the power plug to make sure it is warm, this is another method of making sure power is getting to the computer. If the laptop is powering on but getting a beep code it could be something different and not a power related issue.
If the power plug for the laptop appears to be good then it’s likely that the Laptop power board aka power inverter board and/or system board is bad in the laptop. Now replacing these parts is not easy but it’s not impossible (assuming you have hardware skills). The difficult part is going to be obtaining the parts from Compaq and/or additional details about repair.