If your residuals are non-normal, it suggests you have an omitted variable and are subject to omitted variable bias. You are right about being concerned with normality test failure.

Given that you are using box jenkins methods, I would first look to see if the PACF reveals any other seasonality or higher-order autocorrelation.

One thing I would suggest is to test the possible existence of a structural break. EViews has the Andrews test and newer versions (7 and 8) should have Bai Perron add-on in 7 and built in version 8. There could be change in regime or outliers that are confounding your test results.

Also look at the nature of the non-normality. Are the residuals skewed? Is there excess kurtosis.

I'd also run the RESET test to see if there are significant nonlinearities.

Not knowing what your dependent variable is, nor the goal of the model (forecasting?), I can't really offer more help.

Thanks James

do you think that the SARIMA models should pass most of diagnostic tests, LM test, ..etc , or it can be possible to use the models if it pass two or three test and fail in others? what do you think?

You're welcome. Well, SARIMA are just atheoretical time series models. If those characteristics (autocorrelation, seasonality, etc.) are prevalent in the data generating process, the adequately specified regression would show normal residuals. Non-normality would suggest some significant omitted variable.

Failure of multiple tests poses an uncertainty with respect to what can be done next. It depends on the situations - what exact tests are being failed and what are you trying to do with the model. If it is a pure forecasting model, and the need to interpret coefficients is unimportant, then you would not care so much - other than just worrying about a general mis-specification.