Embedded Database for .net that can run off a network
SQLite came to my mind while reading your question, and I'm quite sure that it's possible to access it from a network drive if you keep yourself to the constraint of 1 user at a time.
I'd recommend Advantage Database Server (www.advantagedatabase.com). It's a mature embedded DB with great support and accessible from many development languages in addition to .NET. The "local" version is free, runs within your application in the form of a DLL, requires no installation on the server/network share, and supports all major DB features. You can store the DB and/or application files all on the network; it doesn't care where the data is.
Disclaimer: I am an engineer in the ADS R&D group. I promise, it rocks :)
It sounds like ADO/Access is perfect for your needs. It's baked into the MS stack, well seasoned, and multi-user.
You can programatically create a DB like so:
Dim catalog as New ADOX.CatalogCatalog.Create("Provider=Microsoft.Jet.OLEDB.4.0;Data Source=\\server\path\to\db.mdb")You can then use standard ADO.NET methods to interact with the database.