We have our source code stored in Kiln/Mercurial repositories; we use MSBuild to build our product and we have Unit Tests that utilize MSTest (Visual Studio Unit Tests).
There's always BuildBot which I like (and have contributed some code to ). It's fairly easy to set-up and run on any OS, and to do simple tasks like that you say, and remarkably flexible if you need it.
What you might find missing is batteries-included log-scrapers and/or report generators that other more commercial CI-servers comes with, especially for Enterprise-y frameworks.
It scales pretty well too, Mozilla and Chromium use it, amongst others.
TeamCity, from JetBrains, the makers of ReSharp, will do all of that. You will have to configure it for what specifically it means to "build your product", but you can configure up everything you specified with it.
The software can alert you to failed builds, even down to alerting only the person responsible for checking in code that broke the build. It even comes with handy web pages you can view to see only your own changes, which builds they've been through successfully, which ones are pending, and which ones are currently being executed.
Since it is a distributed product, you can make it grow with your organization and product. If at some point you discover that you're waiting for the build to complete too much, because a lot of builds are being queued up, you can add more build agents. The build agents are basically separate client programs you install on additional machines, that execute the actual build configurations.
It comes in two flavors, the professional version and the enterprise version. The professional version is free, can contain up to 20 build configurations, 20 users, and 3 build agents. The enterprise version has unlimited users and build configurations, and you can also use LDAP based security (think domain verified users.) There's also some other bonuses from the enterprise version. You can also buy licenses for more build agents if you need more than the initial 3.
Now, if "no server components" means you don't want it to act like a web server, you're going to be hard pressed to find something that will react to your commits.
However, if you mean that you don't want to have to install a server OS, then TeamCity can work on workstation versions of Windows as well. That isn't to say that you shouldn't consider setting up a proper server for it, but it will run on a workstation if that is what you require.
What you've described is the basics of a CI Tool, so every CI Tool should be OK.
I use Cruise Control.NET but it is bugged with Mercurial and is not very straightforward at first glance. I am nevertheless happy with it. Other tools that come in my mind are Hudson, Team Build (from TFS) and TeamCity.
I have not tried other tools but you can see pros/cons here :
EDIT : I forgot to mention that Hudson and Cruise Control.net are Open Source project, you can easily write plugins and patches to your install.
EDIT² : Mercurial bugs seem to be fixed in the upcoming 1.6 version of ccnet (changes commited to the trunk this week).
Our product BuildMaster does all of the things you listed by design and there is a free, somewhat limited edition (e.g. you can only have a limited number of issue tracking providers integrate with it, the database change script packaging tool isn't included in the free version, etc.) for 5 users or fewer.