You're quick Nigel. Thanks for the response. I tried increasing the Prog Delay as much as possible and lowering Vpp delay, but it is still not programming. The 877a does not have an internal oscillator either, so the Vpp delay should not be an issue (although I thought it might be an issue for the 628a).
By the way, I tried changing these values in both the 1.91 and 1.95e versions of WinPicProg.
I am also having a weird issue with the WinPicProg software. When I go to the hardware setup (in both versions), it allows me to set each pin to high or low by clicking on the buttons at the bottom. If I go to Programmer Type and click on P16PRO40-7406, though, I can no longer click on the buttons. The buttons are there, but they don't do anything when I click them.
In addition, in the beta version, there is a setting for MCLR whenever I open up the hardware setup (even though P16PRO40-7406 is already selected). If I click on the programmer type again, that column disappears, and I can no longer click the buttons to set the pins high or low. That is probably a bit confusing, so let me know if I can clarify more. See the screenshots that I have attached.
Thanks!