I do not think internal reinforcement is possible in a damaged, corroded or cracked beam. Only external reinforcement can be done after repair of the damaged beam.
I have reinforced many steel structural elements over the years. Most of that reinforcing was done by welding structural shapes (usually plates) to the parent (damaged) element. Structural steel shapes can be reinforced under load or unloaded. There are some considerations that need to be added for loaded structures. I have also bolted on plates to reinforce steel beams. A cracked structural steel shape may be a different issue. You can research Ray Tide to find a lot of articles on reinforcing structural steel. I would suggest you obtain the AISC Design Guide 15 AISC Rehabilitation and Retrofit Guide as a starting point. Chapters 3 and 4 would be good for you. You will also find great references in Chapter 5.