I'd bet 95% chance the drive is gone and the board still OK. Seagate was a good HDD vendor very long time ago, nowadays they produce crap, same as WD. I'd give a try with replacing the HDD.

The question is why did the monitor PSU melt ? I would guess the monitor has just almost a short on the power supply inlet, and your laptop PSU might have an OC protection, contrary to the melted monitor PSU. However this is a probable reason, it must not be true, and the plug/inlet are not compatible, however I have not the right knowlege about this.

If you have the melted PSU you might transplant the plug from the melted PSU with a short part of the cable on the working PSU cable and see then if it works. Or just cut off the cable frm the melted PSU, connect it to a ajustable voltage...