Option 1
Make a copy of the current .sln and delete the SQL db projects; then point TeamCity on this sln.
Option 2
Create a new build configuration (you have Debug, Release and you can add DebugCI as an example) and mark the projects that you want to compile in this configuration. Then in the build step, enter DebugCI in the Configuration field: (this is debugging in this screenshot, but you get the idea)

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