I found the solution to my problem, but I am anoyed that there is a trap like this.
I have a controller that uses the tiny13. I programmed it using ISP. A week later, ISP would not work. Whatever I did, AVR STudio said "entering programming mode: failed". The problem was the six pin connector was backwards. This should be the first thing you check, but I assumed that if the ISP LED works, the connector is right. I has reset pulled to 5 volts with 27K and PB1 pulled low with 27K and this was enough to run the ISP.