Any thoughts on making this even more awful?

RubeGoldbergSearch.java

  public static int search(Integer[] arriArrayToBeSearched, Integer iItemToBeFoundInArray){
		int iIndexOfItemToBeFoundInArrayInArrayToBeSearched = -1;
		int iLengthOfArrayToBeSearched = 0;
		int iTemporaryVariable = arriArrayToBeSearched.length;
		while (iTemporaryVariable > 0) {
			iLengthOfArrayToBeSearched += 1;
			iTemporaryVariable -= 1;
		}
		for (int indexInArrayToBeSearched = 0; indexInArrayToBeSearched < iLengthOfArrayToBeSearched; indexInArrayToBeSearched += 1) {
			Integer iMemberOfArrayToBeSearchedAtCurrentIndex = arriArrayToBeSearched[indexInArrayToBeSearched];
			boolean bMemberOfArrayToBeSearchedAtCurrentIndexIsEqualToTheItemToBeFoundInArray = iMemberOfArrayToBeSearchedAtCurrentIndex.equals(iItemToBeFoundInArray);
			if (bMemberOfArrayToBeSearchedAtCurrentIndexIsEqualToTheItemToBeFoundInArray) {
				iIndexOfItemToBeFoundInArrayInArrayToBeSearched = indexInArrayToBeSearched;
			}
		}
		return iIndexOfItemToBeFoundInArrayInArrayToBeSearched;
	}

You could replace those numbers with constants, such as line 3:
int iLengthOfArrayToBeSearched = INITIAL_LENGTH_OF_ARRAY_TO_BE_SEARCHED;

You can move indexInArrayToBeSearched out of the for(), Make a int iNextIndexTobeSearched outside the loop, assign it at the top of the loop to indexToBeSearched + 1, and in the last clause of the for(;;), set indexInArrayToBeSearched = nextIndexToBeSearched.

Also, you can special case with if (arriArrayToBeSearched.length == 0) { iIndexOfitemToBeFoundInArrayInArrayToBeSearched = -1; } else { ... the rest of algorithm ... }

Or you could put

if (iItemToBeFoundInArray + arriArrayToBeSearched.length == iItemToBeFoundInArray)
   return -1;

At the beginning.