The Oregon Trail is a series of educational computer games. The first game was originally developed by Don Rawitsch, Bill Heinemann, and Paul Dillenberger in 1971 and produced by the Minnesota Educational Computing Consortium in 1974

Based on the text present on the disk images of the Apple II version, I believe this is the complete list:

• a fever

• dysentery

• measles

• cholera

• typhoid

• exhaustion

• a snakebite

• a broken leg

• a broken arm

• drowning

• AND NOW CORONA!

In particular, I couldn't find any indication that you could die of starvation.