As of today, Microsoft will no longer offer repairs for the original Xbox if the warranty has expired.
A statement from the company
reads, "On March 2, 2009, service repairs for Original Xbox video game systems for which the Warranty has expired will no longer be available. Any other technical support, documents, and content, however, will continue to be available to all our customers. Although Microsoft is ending repair services for the Original Xbox, an upgrade program and support will be maintained for Original Xbox consoles that are still under Warranty."
For those with a machine that
is still under warranty, however, Microsoft states, "If you have an Original Xbox console that is in Warranty that requires a repair, you will be able to submit an exchange request for an upgrade to an Xbox 360 gaming console online."