Calculate Field with Python Issues (If statements)

In general your condition statement should go as:

if TEST1 == 'FAIL':
    return 0

Single or double quotes for checking fields with string values, and when returning to a numeric field no quotes needed.

If I'm reading your logic correctly, if either Test1 or Test2 = FAIL, you want to return 0, but if both = PASS you want to return 1. I'd do something like this:

def Final(t1, t2):
    if t1 == 'FAIL' or t2 == 'FAIL':
        val = 0
    elif t1 == 'PASS' and t2 == 'PASS':
        val = 1
    else:
        val = 2   # this allows you to check if t1 or t2 had some other value
    return val

You could use a dict structure ({key: value}) to convert keywords like PASS to the standard bool type (i.e., True and False). After this conversion to bool, it is conventional logic:

def Final(t1, t2):
    c = {'PASS': True, 'FAIL': False}
    t1 = c[t1]
    t2 = c[t2]
    if t1 and t2:
        return 1
    else:
        return 0

Note that if you have other test values like GOOD or Pass, you will see a KeyError, so you can extend the dict structure, if necessary, to other synonyms that are either True or False.

Also since you have so few combinations check this logic using nested if. No code def required...not tested but you can play with the logic

"0" if !Test1! == "Fail" else ("0" if !Test2! == "Fail" else "1") # python of course