Web Hosts & DSNLess Connections

Is it possible for third party web hosts to disable any kind of connectivity to an access database? For instance, for close to a year I was able to connect to an access database via a dsnless connection. Last week they had problems with their servers in which they had fix. Now I am unable to connect to my db at all. I called them up to ask what's going on and they said that I needed to have a system dsn set up in order for me to have any kind of db connectivity. I always thought that with IIS4 & ODBC, you have the option of a System DSN, File DSN, or DSNless connection. Here is the error I am receiving:

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Please respond back, this problem is affecting 4 other sites of mine. Thanks.