Keep getting invalid API code even though I have logged out and back in again on this site and on ebay. This happens both with the SlamIt! button and when I enter manually on this site. Have tried this with a couple of auctions today.

Hello,
Just follow the instructions in the big blue box to log out and log in again. If you have any issues after that please let us know.

I think I just expressed that I already did that - I have done it multiple times and am not having any luck.

Yes I did miss that, sorry about that. It does appear that you are entering the wrong password because eBay is returning the message, "Oops, that's not correct." We just submit the info the same as it is entered.
If you are 100% certain the password is correct, then the next step is to ensure that you do not have a problem with your eBay account, generally it's an expired credit card message.
Then finally, when all else fails, you could change it at eBay and then use that new password here.
Please let us know how this goes, we'll watch for your reply.