As stated in download page:
openfire_3.7.1_all.deb "Debian package, no Java JRE... "
It is for Debian not for "Debian like" systems, so it probably doesn't work on Ubuntu systems at all.
I have an openfire 3.7.1 working on Ubuntu 12.04 using the unix tar.gz package:
openfire_3_7_1.tar.gz "Works on most Unix variants, no Java JRE..."
It includes a "documentation/install-guide.html" with the package (please read it)
I'm going to resume the installation procedure I made (See result in screenshot):
1) Download and make a fresh installed Ubuntu 12.04 Desktop Edition for 32 bits.
2) Download and install jre-6u33-linux-i586.bin (jdk is not need just jre):
Get it here (or google for it):
Then set it up:
chmod +x jre-6u33-linux-i586.bin
mv jre1.6.0_33 /opt
3) Download and install openfire openfire_3_7_1.tar.gz
tar xvfz openfire_3_7_1.tar.gz
mv openfire /opt
Go to the openfire folder and continue with the rest:
Uncomment and modify the following line at the beginning of "/opt/openfire/bin/openfire" script to override "JAVA_HOME":
WARNING: This is not need if "echo $JAVA_HOME" point to a valid ORACLE Java 1.5 (or later) or OPENJDK installation path. Openfire does not works with "gcj" which can be installed on Ubuntu, check installed version executing "java -version".
Then just start it!