I don't have any kanji reference books so I have to rely on kanji sites for kanji information.
A lot of websites list 入 （いる） as the radical for 全:
just to name a few.
But, two sites, which seemed pretty reliable to me up until now, list 人 （ひと） as the radical.
I'm more inclined towards 入 right now due to the number of sources saying so, but I want to make sure.
Although there have been many sets of radicals and many classifications over the years, the traditional set of 214 radicals is now usually identified with the famous 康煕字典 (Kangxi Zidian). To many people, if you say the radical, it's understood that you're referring to the traditional Kangxi classification.
From that point of view, the traditional radical is 入. See the 康煕字典 online, page 126.
In the case of 全, however, the simplified Japanese 新字体 (new character form) uses 人 rather than the traditional 入, so it's natural for some modern dictionaries to classify it under that instead. I have three paper character dictionaries that use the radical system, and all three place it under 人 rather than 入.
From this point of view, the modern radical is 人.
Of course, it's quite possible for different dictionary editors to classify characters under different radicals. But I think the above is a decent description. As you can see, in this 漢和辞典 published by 学研, both the modern and traditional radicals are listed, corresponding to the modern and traditional forms of the character:
(Revised)
According to this site (http://www.saiga-jp.com/cgi-bin/dic.cgi?m=search&sc=0&f=0&j=)the radical is やね, which is Japanese for roof. I don't think this is one of the traditional 214 radicals (http://kanjialive.com/214-traditional-kanji-radicals/) but it does get used by Henshall in his book "Kanji: Remembering the Japanese Characters".
According to 学研監修漢字辞書 (a real dictionary) the radical is 人 (ひと）.
I don't think you can get a definitive answer unless you go by one dictionary: There are several sets of radicals in existence, compiled for different dictionaries (see also note by Choko). Other users of this site can explain etymologies at great length, if that it what you seek.
Personally I used to find radicals quite useful to look up characters but I can live with 全 having both of these as radicals.
From Chinese character point of view of things the radical is definitely 入 (even though it is written 人 on top!).
Why?
While I'd take the following with a pinch of salt, I still think it's worth considering:
Etymology (文字來源): Remnant Primitive, all of a persons stuff 工壬 under one roof 入 - complete -Chinese Etymology
