Attiny projects?

Okay...I changed the boards.txt to stk500v1, and it worked!

Excellent!

Uploaded the blink sketch successfully and tested it.

Also excellent!

Then I tried the fade sketch, and I got
Code:avrdude: please define PAGEL and BS2 signals in the configuration file for part ATtiny85

I believe that particular error can be ignored.

To "fix" this problem, you need a newer version of the AVRDUDE.CONF file (or you can modify the one you have). In my case, I'm using the latest version of WinAVR. It was easy to get working and solves a few other problems.

avrdude: verification error, first mismatch at byte 0x0008
0x47 != 0x45
avrdude: verification error; content mismatch

That problem will have to be addressed. Unfortunately, it is not one I've ever encountered so I will only be able to offer general advice.

Then I tried to go back to the blink, and get the same error. I unplugged everything and closed the IDE, even rewrote the ISP sktech to the uno.

That was a good first step. You've confirmed that the "programmer" is very likely not the problem.

Same error, tried a second attiny85, loaded the first sketch fine, then got the error uploading the second sketch...

That was a good second step.

any advice?

Yes. Try again with no "devices" (LEDs in your case) connected to the target (the 85 processor). It is very important that the programmer and target are able to drive the three ISP lines to VCC (five volts). Any load on the pin (like an LED) can be a problem (a piezo with no resistor wreaks havoc). Once you have a working setup, you will be able to experiment with what loads you can get away with.

In addition, make certain that you've wired everything correctly, there are no loose connections, and that the wires aren't "too long" (a few inches is good; a few feet is OK; a few yards is bad).

I read that a noisy power supply could have caused this, so I installed a 10 uF cap to filter the power with no change, all in a breadboard, no soldering...

Are you powering the target (85) from the programmer (Arduino)? How is the programmer powered? USB?

In the long term, you will want to include a 0.1uF capacitor across GND and VCC on the 85 processor as close to the processor as possible. The processor will run fine without it (you don't need to add it now) but it dramatically reduces the digital noise (e.g. the analog-to-digital converter behaves much better).

I just find it odd that I can upload one sketch but not another...

That is odd.