The part you got is really BA033FP. The "FP" letters are omitted on package since it is for TO-252 package. The others digits you see are just the manufacturer's codes for wafer lot / factory place / date of manufacturing ... which in turn are not your concern.
Suppose you are badly skilled in soldering, although TO-252 is not really small for an amateur, so you might kill the first part, but for the second one, you might not since your skill was improved from the first one !!!.
Just use your DMM in "ohm range" or "diode test range" to measure the resistance between input and output pins in 2 ways of applying test leads, if the resistances are small and almost equal, so the part must be dead. If the resistances are large (a few hundred kiloohm or megohm), so maybe part is good.
The datasheet you get is not in details, so I do not understand if it needs the minimum load (many voltage regulators need the minimum loads other than 0 (open output) to work well). Try to put at output pin a resistor of about 330 ... 620 ohm to make the minimum load (5... 10mA) to regulator and then measure the output voltage.