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1. for "Condition: B or C has a value" put the below formula in the formulas section and give the range $A$2:$A$5-
=IF(OR(ISBLANK(B2)=TRUE,ISBLANK(C2)=TRUE),"True","False")

2. for "Condition: B and C has a value" put the below forumla and give range $A$2:$A$5 -
=IF(AND(ISBLANK(B2)=FALSE,ISBLANK(C2)=FALSE),"True","False")

3. for "Condition B and C and D has a value" put the below formula and provide the same range
=IF(AND(ISBLANK(B2)=FALSE,ISBLANK(C2)=FALSE,ISBLANK(D2)=FALSE),"True","False")

Select the desired color for each condition.