Michel,
I too have recently upgraded to Absoft 10 (though at present it is still under evaluation in beta mode on a separate pc). Likewise I encountered numerous errors with the "linking" aspects that were not there hitherto.
I took the view that if something worked with a previous version of Abosft then it should work with version 10. In all instances I contacted the support team at Absoft (usally by email as I am based in the UK) and they always managed to produce an answer that was helpful and accurate.
I have checked back and the specifc error you refer was not one of them - in fact I don't seem to have a LIBC.LIB (though I do have a LIBCMT.LIB and a debug version LIBCMTD.LIB in the c:\Absoft10\lib folder).
I remember reading somewhere that you can actually switch OFF calls to spurious libraries by entering the option -v /NODEFAULTLIB:libc.lib (however I have tried entering this in the GUI and encounter all sorts of other LINK errors, so clearly there is something wrong with the format). Nevertheless, your reply from Absoft may be along these lines.
Failing the earlier suggestion and anything from Absoft you could try looking at the results from a Google on LIBC.LIB. I tried this earlier just with key wording libc.lib and there are loads of references to the error LNK1104. The first one, on the MSDN forum, has numerous suggestions mainly related to Visual Studio. The final comment on the MSDN forum (which will not be of any assistance) was done on Christmas Day so clearly this may be a burning issue.
Likewise Seasons Greetings and all the best for 2008.
Mark Coxhead