MSDE - I haven't come across that in a while, that dates back to SQL Server 2000! (MSDE was replaced with SQL Server Express in 2005, so you're a bit out of date).
Anyway, MSDE runs as an NT service, and every service (at least up to Windows Vista) runs under a user account: often one of SYSTEM, NetworkService, or LocalService (Windows 7 and later introduces the concept of Service Identities, which is complicated). You can also run a service under its own user identity, which can be a built-in principal like SYSTEM, a local user account, or a domain account.
I've forgotten the defaults that MSDE uses, but considering it was made in 1999/2000 before NetworkService was invented, it probably runs under SYSTEM or LocalService. To be sure, check your Services.msc
listing.
As for the failure-to-connect, that could be caused by anything: firewall, configuration error, etc, not just a wrong service identity.
So anyway, check your services.msc
and your Application Event Log, then report back with your findings.