As ever, fuses blow to protect the system when a fault occurs - doesn't matter if it's a 'real' fuse or a fusible resistor, it's still a 'fuse' and blows for a reason. Replacing it won't change anything - it'll just blow again until the fault is fixed.
It's value (I reckon it's 51 ohms) will be such as to limit switch-on surge which itself is as a result of the current being drawn by the circuitry and the value of the smoothing capacitor just under the bridge rectifier, presumably C1 (as I can't see the proper designation).
Typical faults to cause the fused resistor to blow include a blown rectifier ('DB'), shorted capacitor (C1) or further into the circuitry like the main controller chip (IC1).
Less often, the actual circuitry being powered by the power supply (one half of the board is power supply, the other is the 'rest' of the circuitry) can develop a fault and cause an overload BUT the controller IC (IC1) usually detects this and shuts the device down anyway so it's likely that everything else is OK and the fault is restricted to one of the parts in the previous paragraph.
Either way, it's going to be a pretty long and complicated repair for anyone not familiar with such - if you can source the parts and make the repair(s) then it's probably fixable but without experience you are likely to make more problems than you solve.