It's not clear that Albacore was missing. The error message indicates that TeamCity cannot find Rake itself!
Cannot start build runner
What was the exact Rake task configuration? Specifically the Ruby Interpreter configuration section? You can tell TeamCity exactly which Ruby to run, which will affect which gems are available (and Rake is just a gem).
It looks like you have a Ruby 1.8.7 installed and that you must have installed Albacore
cmd> gem install albacore
Do you also have Rake installed? In Ruby 1.8.7, the Rake gem was not included by default. You can list the machine's installed gems by
cmd> gem list --local
You'll should install Rake.
cmd> gem install rake
I'm not actually sure how you ended up getting this to work. What's the contents of the batch file? Do you have any other Ruby/Rake installed?