Contacting Mean Well won't help. This board is just using one of their DC-DC modules. Unfortunately, the traces connected to R4 are on the other side of the board. I'd guess that resistor is in line with the fuse and DC input, and is used to reduce the inrush as the electrolytics first charge. Judging from the discoloration, it's been running hot for a while.
/mike
So it was most likely a fraction of an ohm, and the value wouldn't be critical. Maybe 0.5 ohms.
Take the input voltage and divide by 0.5 ohms. That will be the inrush current. If you think the inrush can be higher, make the resistor smaller (less resistance). If you think it needs to be lower, you can make it larger.
Also, and this is important, make sure the power rating of the resistor works using I^2*R for the input current. I would also make sure its adequate for the surge current that will happen when its first turned on using V^2/R with the full input voltage across the resistor.
Lastly, not sure why the fuse didn't blow before the resistor did. There still may be something else wrong - maybe one of the filter caps are going bad, or might be shorted. But you would think that would take out the fuse first.
