No, you generally cannot open the hood of a 2006 Chevy Trailblazer (or most cars) from the outside if the interior release is broken. The hood latch mechanism is designed for security, and there's no external override. You'll need to access the latch mechanism from underneath the vehicle or possibly through the grille (depending on how the latch is constructed), which would require some disassembly and potentially cause damage.
If you're not mechanically inclined, it's best to call a locksmith or a roadside assistance service. They have the tools and expertise to open the hood without causing further damage.
