@Algae said:

I changed it to a / delimiter and it did not notice any difference--still get the link error

This would not have done anything related to the linker error, just a comment.

The file I believe I'm linking to is named libtcl.dll.a

Then I suppose it should be tcl.dll. I should have paid more attention, since it says "file format not recognized" it does mean that it finds the file, thus your link command is correct.

Might it be that you are trying to compile with 32-bit compiler and link to 64-bit lib?
This is just a guess, I see you say you use cygwin 64, just check the architectures.

Apart from these comments I don't think I can help, sorry.