A client wants to \"Web-enable\" a spreadsheet calculation -- the user to specify the values of certain cells, then show them the resulting values in other cells.
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Although this is certainly possible using ASP.NET, it's very inadvisable. It's un-scalable and prone to concurrency errors.
Your best bet is to analyze the spreadsheet calculations and duplicate them. Now, granted, your business is not going to like the time it takes to do this, but it will (presumably) give them a more usable system.
Alternatively, you can simply serve up the spreadsheet to users from your website, in which case you do almost nothing.
Edit: If your stakeholders really insist on using Excel server-side, I suggest you take a good hard look at Excel Services as @John Saunders suggests. It may not get you everything you want, but it'll get you quite a bit, and should solve some of the issues you'll end up with trying to do it server-side with ASP.NET.
That's not to say that it's a panacea; your mileage will certainly vary. And Sharepoint isn't exactly cheap to buy or maintain. In fact, short-term costs could easily be dwarfed by long-term costs if you go the Sharepoint route--but it might the best option to fit a requirement.
I still suggest you push back in favor of coding all of your logic in a separate .NET module. That way you can use it both server-side and client-side. Excel can easily pass calculations to a COM object, and you can very easily publish your .NET library as COM objects. In the end, you'd have a much more maintainable and usable architecture.