Doesn't turn on

@kwakupeter start off by connecting an external monitor and see if that shows. If so it is possible that you have a bad LCD. If still nothing shows and if none of your LED's blinks or comes on at startup then this could be a power issue.

Start off with the easy things. Disconnect the power from the computer by unplugging the power cord from your computer. Disconnect all external devices from the computer. Remove the battery. Now hold the power button depressed for about 30sec-1min. Reapply the AC power adapter and see if your computer does show any sign of life.

Next you want to check your power supply. Make sure it has the proper voltage. Check to make sure that connectors are not bend etc. Check the DC-in jack of your laptop. Make sure there is no corrosion, debris etc. that prevents it from working. Clean it of any debris etc, use a few puffs of air to clean it out. If none of this works, get an ammeter and see if your laptop draws any amperage from the charger. After that, you need to check and see if your motherboard even gets power. For that, of course, you need to open it up. Post Some good pictures of what you see. That way we can see what you see. Aggiungere immagini ad una domanda

Of course, it is also possible that this is a bad RAM module or a bad LCD. So remove the RAM, clean the contacts with a pencil eraser. Do it gentle so as to not destroy the module. Replace it and restart. If you have more than one module, remove it and just leave one connected.

Here is the Compaq Presario CQ58 Maintenance And Service Guide

Let us know how things are working out with each check/test.