Many Thanks everyone....
Tried all the suggestions above, except opening the enclosure and fiddling around with whatever wires may be inside, but still nothing except the ' in use ' light....
All a bit of a bugger, but not a huge disaster - just some music from ex-colleagues that I'll lose and probably won't be able to get again....
Suppose I'll have to buy another one, but fairly sure it won't be Seagate next time....