First thing you look at is the variance of outcome and input. If any of them are 0 then the coefficients are zero. After that lets go on.
Do I need to transform this? Probably not. Ask your self if it make sense that the underlying relation are linear in the current form. For example imagine I want to investigate the effect of wealth on happiness a linear scalling does not make sense 1 dollar does not have the same effect for Bill Gates as for the musician on the street. Here a relative scaling are preferred, so you perform a log-transformation.
Transforming the outcome. Sometimes it can be relavant. The most obvious tranformation is to use logistic or multinomial regression if you have categorical variables. Not doing it is quite wrong.
The next thing you do is you ask your self can my y be independent of this variable? Use your commen sense and your domain knowledge.
There can be reasons why a coeficient are different than it should be. These group into 2 groups:
Correlated variables mess the results up. If you have 2 variables that are highly correlated it is difficult for the regression to find out variable actually made the difference.
There are reverse causality. For example I want to investigate the effect of going to a psychiatrist. I am stupid so I look at the suiciderate of the persons going to a psychiatrist and the persons not going. I find higher suiciderate for the persons going to a psychiatrist. This is not because going to a psychiatrist makes me want to kill myself, but because wanting to kill my self makes me go to a psychiatrist. So the causality is reversed.
So in your case you should look at the variables highly correlated with the variable of interest. Ask your self are there reverse casality? And what variables would have been nice include to explain the problem better and how might they have an effect. Remember finding something is insignificant is also a result.