Replace unknown inductor
The inductor is unlikely to be limiting the current to the ICs, but it may be keeping their noise out of the power supply, or keeping supply noise away from the ICs, perhaps to reduce RF emissions.

As such the actual inductance would not be especially critical, but the DC resistance of the replacement should be similar to the original. Can you measure that? If the failure is such that you can't, your options are:


keep looking for documentation on the machine (Google and persistence)
Find a replacement board (eBay is your friend ... sometimes)
Find a second machine and measure the resistance of it's inductor
if there's an identical looking L on the existing board, assume it's the same and measure that
guess ( and go for something reasonable like &lt;1 ohm series resistance)


EDIT:
This link shows 6 candidates from Farnell with 0805 package and 0.7 to 0.8 ohm resistance. Inductances cover quite a range, you may narrow it down by comparing with yours. In any case, I think yours will probably work, subject to its current rating being greater than the current draw you measure through it.