I finally managed to create a working virtual pet complete with life, sickness, happiness, hunger, and weight. Also its Mumbo Jumbo because it's really easy to build his face.
There's a bit to go over, but let's start with the user interface:
The lectern is just an instruction book, but the button is a reset button. When pressed, the lamp will turn off (meaning you can't press it until it turns back on) and all of the stats will be reset to half (except for life, which will be set to full). The lever is a shut-off switch so the pet's stats will not deteriorate until you turn it on again. The lamp is to show whether or not it's on.
The bar on top is the life meter, and if it drops to zero your pet has died and you have failed as a pet owner.
The bar on the far left is weight, which is increased through food. The pressure plate underneath it is to exercise and lower weight. If the weight drops too low, the hunger will rapidly drop, and if the weight is too high, the happiness will rapidly drop.
The next bar is the hunger, and if it gets too low, the pet will die. In this case, there will be very, very loud "stomach rumbling."
The hoppers out front are where item inputs go.
The next bar is happiness, and if it gets too low your pet will refuse to eat and will cry. You can increase happiness by giving your pet items like diamonds or redstone.
The next bar is sickness, and if it gets too low, your pet will die. Since potions are non-stackable, you need to use gold-plated food items as "medicine." Also, feeding your pet random garbage will lead to it getting sick. Also, puking.
That's about all there is to the machine itself, so here's the circuitry:
There's a lot going on here, but essentially the way this works is item filters (just behind the camera) go into pulse multipliers that move items from one dropper into another, where they are measured by a comparator and go into the lamp indicators. At the same time, hopper timers move items back out of that dropper. The cyan circuit is for the reset button.