By significant vs. insignificant do you refer to their magnitude? What about their p-value? Did you check for multi-collinearity? I need more input in order to provide an intelligent suggestion. Can you tell me more?
I suspect there is multicollinearity which gives rise to only one significant t value. You may like to check correlation and VIF and then treat multicollinearity either by eliminating any variable or increasing sample size (if possible) or going for other procedures like factor analysis.