My theory is that Rand is the human incarnation of the Great Serpent.

Early in the series, the forces of the Shadow (read: Ishamael) referred to blinding the Great Serpent. As the series progressed (especially the latest book), it appears that Rand was indeed blinded in some way. He even refers to how he was blind but now can see or some such in ToM.

None of this answers your question, though.

From his revelation in tGS and his actions and conversations in ToM, it appears more like Rand may have a connection to all of his past incarnations. This means he is not Rand or LTT, but all of the Dragons that have ever existed.

I would compare it to Birgitte right after she was ripped out of tel'aran'rhiod. She had all the memories and experiences from her past lives.

What makes Rand's situation difficult to understand is the voice in Rand's head. Who was talking to him all that time? Who seized Saidin that one time in KoD?

The answer to that is just as Semirhage stated: he was insane. Rand was already starting to access memories of LTT's life, but due to stresses and perhaps an inability to cope with his fate, Rand's brain compartmentalized LTT's memories and made up the voice as a seperate personality. This personality was able to do and say things that Rand may not have wanted to do or say. After a while, the personality took on a life of its own.

Once Rand had his revelation on Dragonmount, the made-up personality was dissolved.