2000 GMC Jimmy Bad battery connection/car stalls

I have what appears to me to be a bad battery connection and/or issue with the electrical system. When attempting to start the vehicle (either hot or cold), there is no electrical response. If I pop the hood and jiggle the battery connections, I can restore the electrical system, and start the car. Sometimes it fires up right away, sometimes it takes some work (as if the battery were drained).

When the engine eventually fires up, it will run rough for a few moments and smooth out. This has been going on for a couple of weeks now, and I used to be able to drive the vehicle for a significant amount of time (100+ miles). Today, however, if I put the vehicle into "drive", the engine dies. I am able to re-start then engine using the method described above, but it will again die when put into "drive".

Other information that may I think may be helpful:
- When driving, the radio will go silent for a very brief moment and then come back on. It's as if the electrical connection is momentarily disrupted and then restored, but it does not appear to be shutting off and turning back on.
- While driving, the dashboard indicator lights sometimes flash on and off, as they do when the engine is started. These problems do not happen at the same time. Both issues described started within the last week or so, after the initial problem and before the engine dying.
- The vehicle interior lights will not come on when a door is opened, but can be turned on using the switch on the dashboard. This has been an ongoing issue since I bought the car a little over two years ago.

Other information that I don't think is pertinent but I'll add it in anyway since I'm not an expert:
- I replaced the muffler and tail pipe about a month ago, before this issue started.

Thanks for any help!