I read siwiek's latest posts and can explain what happened and how it all works. The real clue is what visa agent told... there is a note in the profile (immigration database). You've been refused entry in Phuket because you had too many tourist visa entries overall or in a short timespan. How many is too many... depends on the mood of IO. This is not related to boarding pass stuff in any way (maybe you misunderstood the situation).
Seems like you were not denied entry in Nong Khai, they just cancelled your exit stamp from Lao side, right? Every immigration checkpoint as every Thai embassy overseas is different in their policies so you might get lucky when you try another entry point, nothing stops you from that, you're not blacklisted. Get tourist visa in Vientiane, fly to Kuala Lumpur then fly local to Alor Setar, take Grab taxi to KTM station then it's 40 minutes to Padang Besar border checkpoint. They will take you to supervisor, tell them a better story about Phuket airport immigration asking to show 20,000 THB in cash and you didn't have that, also you didn't book return ticket at that time. Now you have all that and can show bank account statement, also they can ask where do you work and why do you visit Thailand so often. Prepare your answers beforehand. If they send you back, go try Sadao border nearby. In general, it's better to switch to long-term visa ASAP.