Need some insight into the significance issue

[juan]

I have a factorial design. When I perform the overall main effects and the interaction effects tests, all of them are NOT significant. However, when I use the slice option in PROC MIXED, this is, I asses the effect of one factor at each level of the other factor,  one of these test comes out highly significant. How should I take this? just disregard in view of the overall test non-significance ? or consider further using some adjustment for multiple comparisons?

I am attaching an image of the SAS output for you to see. Notice the overall test output above and the slice effects on the bottom.

Thanks a lot for any lights you can provide!

Juan