Younger home owner here. I've had water get into my basement a few times last spring in the corner and in this area (directly under my little front deck). The corner was due to no downspout (water was all coming down at the corner from the gutters) and this area I believed was due to gutters clogging and doing similar.
I finally killed all the mice and started pulling insulation bats out of the joists to vacuum and bleach and discovered the section of rim joist shown in the video below. I could pull out the bottom wood with my hand. The joist to the left of it has a hole in the sill plate directly to the outside by the deck (shown gap in pictures).
Upon going outside I found a pretty sizable gap along the bottom of the siding which appears to be caused by the sill plate protruding. I'm sure I need to caulk and flash better around where it meets the house anyways but how would I even begin to fix this? Part of me says pull off the deck boards, flash with a z channel if it's not there (including that front door sill plate) and caulk it all up/sawsall the bit of sill plate sticking out and foam/caulk everything together/brace the interior joist but I'm by no means a experienced handyman. Any advice would be appreciated.
Video: It's the bottom half of the wood-the joist to the left is dry/one to the right is braced (may have been previously repaired) but dry.
Pictures: Gap is shown in with board protruding is third to last.