There's power, no booting and no screen, at all.

Hi @collin34227

If you have a DMM (digital multimeter) check if there's 19V DC on the output plug of the charger. If you don't have a DMM then try using a different, known working, compatible charger and check if the laptop indicates that the battery is being charged when the charger is connected to the laptop.

If 19V DC is not available on the output plug of the charger, replace the charger and check if the laptop battery starts to charge when a replacement charger is connected. Allow the battery to fully charge before turning on the laptop.

If 19V DC is available on the output plug of the charger and the laptop doesn't indicate that the battery is charging or connecting a different known working compatible charger to the laptop also doesn't get the laptop to indicate that it is charging, it could be either a faulty DC-In jack (supplier example only) or a problem on the motherboard.

What can sometimes happen is that the centre +ve pin of the jack breaks internally and this opens the power path between the charger and the motherboard, so it receives no power and cannot operate or charge the battery.

To check if this is the problem open the laptop to gain access to the DC-In jack cable and disconnect it from the motherboard. Then use either an Ohmmeter or a voltmeter (both functions are found in a DMM) to check the DC-In jack for continuity between the input to the jack and the cable plug connected to the jack.

Here's the ifixit Disassembling Acer Aspire 7551G guide that will help. See Step.17 for removing the DC-In jack

If the jack is faulty it will have to be replaced as it cannot be repaired. Search online for Acer Aspire 7551G DC-In jack, to find suppliers that suit you best.

If the jack is OK then further testing of the motherboard using the schematics would be necessary.

If you wish to dispose of the laptop, remove the hard drive (HDD) from the laptop. That way you can keep your data. There's information online for how to connect a HDD from a dead laptop, to another PC so as to recover your data.