The definition of Berserk seems to suggest that the berserk character prefers melee hand-to-hand attacks. However, ranged combat is mentioned. If a character with Innate Attack goes berserk, but his enemies are less than 20 yards away, can he choose to use Innate Attack instead of punching people and charging to hand-to-hand distance? If so, I assume he must still use All-out Attack and he cannot aim.
Yes, Prefer Mêlée
If the enemy is more than 20 yards away, you may attack with a ranged weapon if you have one
The 20-yard cutoff point serves no other purpose than as a qualifier for when ranged attacks are allowed. Thus, there would be no point to write in the 20-yard clause if berserkers could use ranged weapons at any range. Otherwise the rule would just say that you may use any weapons, but cannot Aim and may only spend one second reloading.
Furthermore, there's a principle that exceptions written as exceptions imply that the general differs, e.g. 'it is illegal to wear a dragon disguise in the senate building' implies that it's legal to wear it in most other places. Conversely, the permission to shoot beyond 20 yards supports the prohibition against shooting at less than 20 yards.