Was Lin Biao a total recluse? If so how did he get so powerful?

The answer seems to be pretty clear from the Wikipedia entry on Lin Biao.

how did he get any power at all?

I am quoting the same article here:

As a child, Lin was much more interested in participating in student movements than in pursuing his formal education. Lin joined a satellite organization of the Communist Youth League before he graduated high school in 1925. Later in 1925 he participated in the May Thirtieth Movement and enrolled in the newly established Whampoa Military Academy in Guangzhou (Source: Leung 69)

This is shows his innate revolutionary nature to participate into community based movements.

How did he meet with Mao?

Support from Mao's Wiki

Hiding in Shanghai, the CPC Central Committee expelled Mao from their ranks and from the Hunan Provincial Committee, punishment for his "military opportunism", for his focus on rural activity, and for being too lenient with "bad gentry". Source: Wiki of Mao

Wandering the countryside, Mao's forces came across a CPC regiment led by General Zhu De and Lin Biao; they united, attempting to retake Jinggangshan. Source: Wiki of Mao

Returning to Lin's page,

After joining forces with Mao, Lin became one of Mao's closest supporters
Source: Mackerras, McMillen, and Watson. 140

Why did Lin choose to be close with Mao?

During the Jiangxi Soviet and Long March period, Lin, despite his youth, established himself as one of the CCP’s leading military tacticians and battlefield commanders. He became closely aligned with Mao and praised him both in public and in writing; whether this was sincere or a tactical career move is unknown. - See more at: * http://alphahistory.com/chineserevolution/lin-biao/#sthash.wuP7icLe.dpuf*

Well, I couldn't find a definitive proof, my take would be that his nature to revolt made him take sides with Mao and ended up getting trapped in a game of political power!

So, yes, later he realised his initial mistake and it was too late to step out of it, his request to cancel his appointment as the Vice-Chairman was rejected. Source: Qiu The Culture of Power. 78-79

How he rose to power:
You can refer to the section Rise to prominence in Lin Biao's Wiki which describes various incidents where Mao makes preparation to ensure Lin is raised in the chain of command the most significant one being Mao's decision to make him the Vice chairman.

Yes, the account says he was diagnosed with mental illness only by 1953, by the time Mao has complete faith in him.

In early October 1950, Peng Dehuai was named commander of the Chinese forces bound for Korea, and Lin went to the Soviet Union for medical treatment. Lin flew to the Soviet Union with Zhou Enlai and participated in negotiations with Joseph Stalin concerning Soviet support for China's intervention, indicating that Mao retained his trust in Lin.
for more refer to Alliance with Mao section.

A possible explanation for him acting like a psychological basket case (I assume it means psycho :P) other than his mental illness could be:

Because Lin had no real interest in the position of Vice-Chairman, he did little other than whatever he believed would ingratiate himself to Mao. Privately, Lin had no interest in promoting the Cultural Revolution, and attended government meetings only when Mao demanded that he do so. Those colleagues closest to Lin noted that Lin avoided talking about the Cultural Revolution in any context other than public speeches, and when pressed would only make very brief and ambiguous statements. After 1966, Lin made no phone calls, received few visitors, secluded himself from his colleagues, and gained a reputation as being "reticent and mysterious". He did not take an active role in government, but allowed his secretaries to read short summaries of selected documents for half an hour in the morning and half an hour in the afternoon. This was generally insufficient to fulfill the responsibilities of vice-chairman, and he left most important work and family duties to his wife, Ye Qun.
Refer Activities section for more.

I hope this answers your question of a mentally unstable soldier rising to be secon-in-command of the Chairman Mao.