obviously only going on the pictures, its most likely AC, it would make sense due to the full bridge rectified located at D3 (to the left of that large 2200uF cap). however while I could be be wrong id more expect it to be 9v AC input.
you see 12v AC to DC conversion usually provides around 15v DC after the bridge rectifier. considering the 5v DC CPU, logic, ASIC's etc used dropping 15vdc to 5dc not only seems like a major waste it would also get very hot and I see no large heatsinks there to dissipate the amount on waster thermal energy produced. obviously if
id suggest trying with 9v AC before trying 12v AC wall power supplies. also its quite likely you could just feed in a dc voltage regardless due to that bridge rectifier on there, usually 9/12v dc @ 1A would suffice there.
also 4.5v is going to be just to low voltage to work. you would need 5v dc if connected directly to the IC's.
easy solution would be to measure the power and ground on the eprom while feeding voltage into the input jack.
lastly the Focus EtherLan SC-T is basically a Focus rebranded Nuvotech NuvoLink SC (focus bought Nuvolink). if you need more Information perhaps try contacting
@saybur as he reverser engineered the whole device so he should know a great deal more about it all.
not sure how helpful what I said above will be but maybe it'll help point you in the right direction