According to Wikipedia, as of January 2005, it had one airliner, a B737-200, and 2 destinations: NBO and JNB
There is an interesting article from the Uganda Monitor on 27th April 06 which states (the article is well worth reading in full):
The people of Uganda are calling upon our government to re-establish a national airline as a matter of urgency, national interest and pride. Uganda must have a national airline now...Since the unfortunate collapse of Uganda Airlines, our country has lost a lot of money to foreign carriers...Two years ago, three Ugandans Ben Mutyaba, Justin Olwedo Okot, and Ramesh Mashran started the East African Airline. This airline has gone through terrible difficulties to operate up to now. The major difficulty is the stiff competition from Kenya Airways on the Entebbe/Nairobi route which Kenya Airways has monopolised.
A Uganda New Vision article of 26th April 2006 claims the airline has been sold to new owners:
THE owners of East African Airlines have sold out their interest in the airline to new shareholders. A communication to staff said Africa Direct Uganda Limited and Frederick Ochieng-Obbo are the new owners of the airline that has been struggling since it started operations in 2002.