Help Creating Nested IF/OR or OR/IF Formula with Outcomes Based on Several Conditions

I have an "IF" formula whereby if one cell is empty - let's say it is Cell H8, the value in the target cell (F8) is empty, and if H8 has any value, the value in target cell F8 is the date in a different cell, C2. Alone, that formula works flawlessly.

However, I want to run instead a nested IF/OR (or would it be an OR/IF) formula so that if H8 has any value, and another cell, E8, has for example a value of "1", the date in my target cell F8, will not be the date in C2, but a date of "01/01/2014", (thus the "1"). Same with 2 (=02/01/2014), 3 (=03/01/2014), etc.

I cannot seem to come up with the right formula. Excel keeps trying to fix it by inserting a multiplication operand of "*" between the IF logical test and value and the OR logical test and values. And when it appears the formula is right the yield in my target cell just shows "TRUE".

Can someone help? Most grateful, thanks!