No explosives, eh? Well, if you are going to change how chemistry works on your world, people will wonder about basic life processes too. Anyway, other medieval-level advancements could be:
Metallurgy
Longbows, crossbows and ballistas were already capable of penetrating armor, fortifications, and ships. These weapons stored kinetic energy in wood or fiber, not springs. However, consider that the medieval Japanese made vast improvements in steel during this time, albeit with an eye toward sword making. Perhaps blacksmiths could explore making spring-steel, to make better siege engines.
Magnetism and Electricity
Rail guns, anyone? A world without combustion means that propulsive forces are not chemical in nature. Other answers have already mentioned steam and thermodynamic engines (expanding gasses) to do work. Another option is electricity. Static electricity was known to the ancient Greeks, and the compass by the ancient Chinese, and certainly everyone has seen lighting. Maybe in this world the Baghdad Battery was for real?
Ballistics
The study of ballistics began during medieval times, though it was rudimentary. First, there's the projectile itself. Consider that the transition from musket ball to rifled barrels was a huge advance. 1006
Maybe round projectiles were abandoned in favor of darts, with fins that impart spin. Second, had Catholic dogma not held us in the Dark Ages for 1000 years, it's entirely possible that the Renaissance would have happened a lot earlier. This would include the study of physics and the laws of motion, which would improve the accuracy and efficacy of weaponry.
Aerial Attack
The first hot air balloon was not until 1783 but the concept was known by medieval minds. Sky lanterns were known in 3rd century China. <PERSON> and <PERSON> both conceived of hot air balloons. <PERSON> also thought of gliders. (I will ignore other physically impossible man-powered contraptions since they are not feasible.) So, perhaps hot-air zeppelins and aerial bombardment/scouting/command/close air support?
Propaganda and Totalitarianism
I always assumed medieval war was Total War, but what if some medieval <PERSON> realized the true power of propaganda? Certainly ancient Egyptian steles and statues were used to glorify pharaohs and intimidate their enemies, but those did not necessarily motivate entire populations to action. Single-page leaflets and fliers potentially played a significant role in fomenting and focusing the rebels of the American revolution. The printing press and Gutenberg Bible was definitely available since the 1400's. What if the social and political sciences developed to such an extent that lords and governments began to desire and exert not only physical and financial control of its population, but also full totalitarian control of each individual (like the Church basically did). Since the concept of nation-states was still forming at the time, a feudal form of totalitarianism would probably depend more on the cult-of-personality, as we've seen with <PERSON>, <PERSON>, <PERSON>, etc. 1006