first mistake was not disconnecting the battery NEG terminal to disable power. you should always do this unless you are very competent with working on the car, but it's always safe practise to do so.
short circuiting the wiring could have caused any number of problems, more than just a damaged headunit.
do you have a DMM (digital multimeter)? you need one to confirm all the necessary wiring is intact (ie: to check voltages of powerwires). though given the factory headunit powers up suggests they should be ok, but you cannot be 100% sure without testing properly.
use a DMM and confirm the wires supplying power to the headunit are ok. these are in the 'power ISO' plug (one of the black plugs that goes into the headunit; the other is the 'speakerwire ISO' plug, so it should be obvious which is which. the factory headunit should have a schematic stuck to the top of it, showing the wiring pattern. does it? some may not, depending upon brand of headunit.
in the power ISO plug, you need to check the wires #4 and #7 provide +12V. #7 is the 'constant' powerwire, so should give +12V regardless of ignition key position. wire #4 is 'switched', so is 0V with the key at OFF, and +12V with the key at ON. confirm this occurs. note, some alfa's do not have a wire #4.
if these are intact, then the fuses are ok.
what exact brand/model is your current headunit? it should have an inbuilt fuse too, so replace it. it will either be inline with the YELLOW constant powerwire or built into the back of the unit.
depending upon brand, it may also have a 'reset' button that you should try hitting.
let us know what you find.