Invalid device signature for ATtiny84 SOIC package

I'm not exactly sure what is considered a "SPI" device, but two op amps are connected to the SCK and MISO pins. I removed the dual op amp chip from the PCB and programming worked. However, the results were still a little inconsistent. Sometimes, I had to unplug the UNO and plug it back in for it to work correctly (the IDE said "programmer not responding")...any ideas about that?

Also, I'd really like to be able to program the attiny84 while the op amps are connected...will the series resistors make this possible? If so, where exactly should I place them?

Here's the schematic:

https://plus.google.com/u/0/photos/112970352885170654279/albums/5734988209816271265/5734988211154316818