WELCOME TO CHINA! No matter how desperate schools are for foreign teachers, they always make the foreigner provide their credentials first -- implying some sort of "standard," but soon it is discovered (often too late) that the school/management has no professional standard or integrity on their side of the equation. These types of operations usually offer no professional support (stable internet access, proper teaching materials, etc.)

Negotiation is EVERYTHING in China. Nothing is offered without tenacious negotiation (to foreigners or Chinese).

Yes, 4000RMB is low, but there's no way they'll offer more until they believe someone is worth it. Most Chinese schools or businesses I worked with during my five years there, had no website -- or if they did, it was poorly maintained.

Ultimately, it's the secrecy that's the turn-off, and will likely continue for the duration of your "relationship" with them. I agree with the other poster: move on.