Vehicle non-responsive, then works with no explanation?

Hey, first time poster here! I have a new to me 2005 Prius which has been behaving a big oddly recently. Here's what I recently experienced:
Vehicle was behaving normally, no issues with key fob locking or unlocking, started every time with no issues. Key fob not required to be inserted into slot to start, just inside vehicle. I parked it for a couple days locked, and when I came back it was not responsive to the key fob. I tried locking and unlocking with the fob, no response. I decided to open the driver door with the key insert, but the dome lights and other inside lights did not come on. The unlock button on the door did not do anything, nor did any other buttons inside the vehicle. I tried to start the car, no response. Thinking possibly the battery was dead (although it had been fine before) I crawled into the trunk and pulled up the mats, etc. and used a multimeter to check the battery voltage. Immediately upon connecting to both terminals the vehicle alarm began sounding and lights were flashing. I jumped to the front seat and pressed the power button a few times and got the alarm to stop. I checked the battery voltage again and it was 11.9v, obviously full enough to work fine. After that everything in the car worked completely as usual, starts just fine, key fob locks and unlocks doors, everything is completely normal.

This happened again yesterday, when I returned the car after being parked for several days. I pressed the unlock button on the fob and I heard it make a slight sound, but then no more response to the fob. I opened the driver door (which was now unlocked) and the alarm went off. I pressed the power button twice and then everything was as usual. I have no clue what was wrong or how I fixed it either time, so I do not know if/when this will be a problem again or how to prevent it. Does anyone have experience with this type of issue? Thanks in advance!!