A broken dpkg may make it impossible to install any .deb files. A procedure like the following will help you recover from this situation.
$ links https://http.us.debian.org/debian/pool/main/d/dpkg/
… download the good dpkg_version_arch.deb
$ su
password: *****
# ar x dpkg_version_arch.deb
# mv data.tar.gz /data.tar.gz
# cd /
# tar xzfv data.tar.gz