I have been daignosed with a blocked fallopian tube. what are my chances of conceiving naturally?

Very good: Very good if only one tube is blocked. Sperms need to find a way to get through the tubes to fertilize the egg. The fertilized egg needs to pass through the tube to get to the uterus. One open tube is good enough. However, if the fertilized egg get into the dead end of the blocked tube, a tubal pregnancy may happen.

One tube: If its only one it essentially reduces your pregnancy rates by half, since ovulation generally alternates between the ovaries, however the egg can cross sides but not often. If the obstruction is a "hydrosalpinx" or fluid filled tube then the chances are much lower than that due to the embryotoxicity of the fluid in the tube and needs surgical attention.