I'm not able to get into Applesoft BASIC using ctrl-reset. I also tried running BASIC from a system disk.
The "ctrl-reset" is what you use if you're booting with no bootable media in any drive. Are you saying that you're doing crtl-reset (power key on an ADB keyboard) while looking at the moving boot-bars and it's not dropping you to the prompt? That's... unusual.
Anyway, given the evidence here I'm totally going to venture that your Mega II chip is bad. The close-up photo of your display shows that the top four rows of pixels in each character are being doubled into the bottom four lines of each 8 pixel tall character cell. The text display on an Apple II (and most other machines with "character-based" display modes) is generated with the aid of a counter which is connected to some of the pins on the character generator ROM; for instance, in the case of a "real" Apple II with discrete components a 3 bit "row counter" is connected to A1-A3 of the 2513 character generator while the state of remaining lines is generated by the value fetched from the video buffer RAM. Meanwhile, the output lines from the character generator are connected to a parallel-in->serial-out shift register which is connected to the pixel clock. The dance that happens when generating a line of text characters on the apple II thus looks like this:
1: A "Video Address Generator" circuit walks through 960 memory locations in 24 blocks of 40 linear addresses. (or 1920 cells in 80 column mode, 24x80.) Each block of 40/80 addresses is repeated 8 times (controlled by the 3 bit row counter) before moving to the next block of 40/80.
2: A byte is fetched from the RAM location pointed at by the VAG, and is fed into the high address pins of the character generator, which the low bytes are slaved to the row counter. The output lines of the CG (which is of course just a ROM) produce one line of bits making up the character and shoves them into the shift register.
3: The bits are clocked out as individual pixels. When enough pixels for the character have gone out the VAG updates and the next byte is fetched.
4: When the end of the line of pixels is reached the row counter is incremented and the VAG counts back to the start of the line addresses; once the horizontal blanking interval is over and the electron beam is back at the beginning of the row the same block of characters is run through again, this time displaying the pixels for the next line down.
5: When the row counter rolls over the VAG moves to the next line, allowing the next line of characters to be painted.
6: Wash, rinse, repeat, until all 24 lines have been walked through; reset the VAG and row counter, enter the vertical blanking period, and wait for the next frame.
I think your MEGA II is fouled up so the 3rd line on the three bit row counter is stuck. (Or, perhaps more likely, the address line on the character generator ROM is.) The reason I believe it's inside the Mega II and not elsewhere is because there doesn't appear to be a dedicated "character ROM" address/data bus on the Mega II, which means that either the character ROM *is* internal to it or the data is fetched from the general purpose ROM over the regular bus, and if *that* had a stuck bit the machine almost certainly wouldn't work at all. Meanwhile the graphics modes work fine because in all graphics modes other than the low-res "blocky" 40x48/80x48 ones don't rely on a row counter or otherwise replaying the same block of addresses over and over again.
(Part of me wonders if the "Low Res" graphics are also corrupted, since they intrinsically also involve cutting the character cell in half horizontally; this would point to a different root-cause failure in the Mega II, but likewise almost certainly unfixable.)
