Does it draw any current on the DC input? It should at least draw a little because in the schematics, pg 5 there is a voltage divider of R6002 and R6003 right across the power rail (to derive the AC-detected signal). If FUSE6000 is ok, there should be at least some current flow because of that.
Does the battery pack still produce a voltage on its terminals? If so have you tried running it on battery alone?
I am a bit confused by your pictures. According to the schematics there should be a Littlefuse 451-series 12A fuse in the connection to the adapter socket and similar a Littlefuse 451-series 15A in the connection to the battery pack. According to the Littlefuse data sheet for the 451-453 series, these fuses should be marked brand amp-rating, e.g. LF 12A or LF 15A. Are you sure you have identified these fuses?
Since you have the schematics, your best bet is to use it to find what voltages should be present at various component pins, then identify the components on the PCB and check with a voltmeter. A tedious process but it should help to narrow-down the problem.
With respect to what has gone wrong, it could be anything polarised like diodes or capacitors that got damaged by reverse polarity and after the correct polarity was restored, heated up over 2 minutes until they failed completely. My iniitial suspect was the battery but since you say that the PC doesn't work even without battery pack, its probably something else.