I read the data sheet for ATTiny.I learned a lot about power modes, communication, memory, etc. I have a highlighted copyin my office now.
I started of by noticing that in my scheme, PB2 was connected to LED and PA3 was connected to the button
I remade my board from previous week because I wanted to get better at milling and soldering, and I wanted to be sure that my board was working.
The next thing was to program the board I used the FabISP programmer we had made earlier in the semester to program my new board. I compiled hello.ftdi.44.echo.c and uploaded to the board. Next, I modified hello.arduino.328P.blink.c to program my board. The LED behaved as expected.