OLS regression interpretation when sample means from t-test are insignificant

I tried to search for this somewhat basic question but was unable to find an exact answer. I am running a multiple regression model for time series data using OLS. The dependent variables seem to be insignificant based on a simple t-test where I have corrected the standard errors using Newey-West method. However, when I estimate my multiple regression model (also using robust standard errors), two out of the three independent variables have statistically significant effect on the LHS variable while the intercept remains insignificant (as it probably should be, based on the results of the t-test).

Is there an interpretation for this? I mean, if the LHS variable cannot be distinguished from zero under the usual OLS assumptions and certain confidence level, how are the RHS variables able to explain the changes in the LHS variable? Am I thinking this too hard or missing something obvious? Thanks in advance for any help.