The pink LED is the power indicator, it will be on as long as the device is powered.
On the latest images, the white LED should stay solid at first, but then switch to a heartbeat (two flashes, brief pause, two flashes, etc.) On older images the behavior is actually different.
Alright, so USB serial mode is actually far from the simplest thing to get working. Let’s forget about it for a second, as you’ve tried two other things that didn’t work either.
First, there’s the 3,5mm video out. If this doesn’t work, there’s something quite wrong with your CHIP (either with the hardware of with the software). Did you use a pink cable bought from NTC? If not try plugging the red plug into the yellow input of your tv and vice versa. There’s actually three versions of this cable which all pretty much look the same, but are different in which connection is routed to which connector. One of them just works, one of them works with the red and yellow plugs switched and the final one just doesn’t work (its ground is connected differently), but the first two types are far more common than the last.
Second, the flashing doesn’t work either. I see two things that can help here. One of the problems that the flasher has is that it sometimes get stuck if you don’t restart Chrome. So, if you haven’t restarted Chrome, update the flasher, restart Chrome, then try flashing and if it gets stuck, restart Chrome and try again. (If it gets stuck again, but not at the same point, restart Chrome again and try yet again.)
The other thing that might be causing problems with the flashing is the USB cable. You mentioned you used different cables. However, quite a few cables don’t work for flashing the CHIP and the fact that you were able to use the cable for transferring files isn’t actually a guarantee that it will work for flashing. So, try more different cables. This would also explain why the USB serial isn’t working, so it seems quite likely to me that this is the problem.