My research suggests that the cable is the same but it is based on the information supplied by various vendors I have found on the internet - much like you have. I'd stick to the primary number on the faulty cable and/or the number provided by ASUS
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== Update ==
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Thanks much, Richdave! I took a chance and am happy to be able to answer this question affirmatively: the 14G2235HA10 IS apparently equivalent to the 1422-00ML000 cable.
My research suggests that the cable is the same but it is based on the information supplied by various vendors I have found on the internet - much like you have. I'd stick to the primary number on the faulty cable and/or the number provided by ASUS