Weird issue ESP-01 Blue led lit on 3.3v logic, mega2560

I am having a very weird and frustrating issue with this ESP01. I am creating a shield on protoboard, and everything checks out as far as I can tell. I am using a 3.3v voltage divider (1k and 2.2k) from arduino TX to ESP RX.

When I connect the ESP straight to the arduino Mega 2560, it works fine. When I connect the ESP to my protoboard, the blue led stays lit. Now here's he weird part.
I broke out the protoboard header with jumpers to the ESP, 3.3v to vcc and ch_pd, gnd to gnd in my header and Rx/tx straight to ESP bypassing the header, and serial works.
While still powered up, I moved the tx/Rx to the header, through the voltage divider, and it still works! But when I disconnect USB from the Arduino, then reconnect, the blue led stays lit, until I connect Rx/tx straight to arduino, then back to the voltage divider.
I know pics would help a lot, and I can post some later tonight after work. My wife, sensing my frustration, told me to set everything down and go to work so I wouldn't break anything, so I am asking around for possible fixes for when I get home.

I thought insufficient power may have been an issue, using the mega 's 3.3v for vcc, so I built a voltage regulator circuit converting a 9v battery to 3.3v (well 3.75, using an LM317T with R1=330ohm/R2=660ohm because it's what I had on hand) and there was no change in performance, besides the LEDs being slightly brighter. The ESP still functioned with RX/TX straight to arduino with this 3.75v vcc.

I appreciate any and all replies, and will provide any necessary clarification. I am currently testing my code with a simple serial relay sketch, ESP on Serial3.

I have nothing else connected to ESP besides vcc, ch_pd, gnd, tx and Rx.