Same problem, after the Gift Bag #3 update.
SupportTool.exe file is dated at the time of the update (from Steam).
File EoCApp.exe is NOT present in the DOS2 DE bin folder, only in the classic folder.
Running that one does work and starts classic DOS2.
Win7 64 bit + service pack #1, core i7 950, 24 Gb RAM, GTX 760.
Windows firewall allows all DOS2 (public and private) access to the Internet.
Running under Steam; did the file verification 3 times.
Steam always "re-downloads" a "non-verified" file, but it's the same problem.