Most free hosting sites give you the bare minimum amount of resources to start building a site, but not enough to actually create a production site. They expect you to pay up eventually. They have ridiculously low limits on disk space, database size, etc. If you have an always-on broadband connection, you're probably better off setting up your own web server at home and opening a port on your router firewall to forward traffic to your web server. You can run ASP.NET on Linux using Mono (either in a VM or on physical hardware), so you don't even have to tie up a Windows machine to host it yourself.
If really you don't want to administer your own server, I'd highly recommend going with a very cheap host instead of a free one. For example, 3essentials has plans starting at $4/mo. Unless you're homeless and need that $4 for a month's worth of ramen, I'm guessing you can probably scrape up that kind of money from somewhere.
Also, you might want to consider using MS SQL Server or MySQL instead of Access. Access is great for small, single-user stuff, but it isn't intended to be a full DBMS, so it probably won't scale very well.