Was there any way for Trotsky to win the Political struggle in Russia following Lenin's death? (1924-1928)?

No. The Old Bolsheviks were very wary of him, as they feared a Red Bonaparte. Trotsky ruled himself out of the succession soon after the October Revolution - although that might have just been political manoeuvering.

Stalin played the long game.

When Lenin was alive he was able to use the seemingly innocuous post of General Secretary of the party to fill the highest Party posts with his appointees, and to demote or sack to appointees of his rivals. Trotsky also played into Stalin's hand. He only joined the Bolsheviks in early October 1917, he had been a fierce critic of them when he was a non-aligned Marxist, and Stalin, and the other Bolsheviks knew it. Many never forgave him.

Trotsky's position as the Commissar in charge of the Red Army gave him enormous influence, influence that the other Bolsheviks were very concerned about. They were mostly very widely read, and new the history of the French Revolution, and how a capable military man - Napoleon - was able to use the military to seize power and snuff out the radicalism of the Jacobins.

As Lenin was dying fro the last two years of his life he lived about 10 miles out of Moscow - Stalin controlled all access to Lenin, including vetting Lenin's post. Stalin was, therefore, privy to Lenin's thoughts, and the thoughts of those who corresponded with him.

When Lenin died, Stalin told Trotsky the wrong day for Lenin's funeral - making Trotsky look bad -and like he did not care for Lenin - in front of the other Bolsheviks.

During the next few years, before Stalin played one faction off against each other, the fear of Trotsky turning into another Napoleon made Stalin's task of isolating him and his supporters and eventually of exiling him very popular in the Politburo.

See:

Stalin, A Biography - Robert Service

Trotsky - A Biography - Robert Service

The Revolution Betrayed - L Trotsky

http://www.trotsky.net/