Might help you get more accurate answers if you named the specific display you're using. Some of them have attachment points, and some of the more popular ones (Adafruit's PiTFT's for example) folks have already built cases for that you can work from.
With the combination of battery and screen, it's unlikely any straight off-the-shelf solution is going to work well. And Legos over the screen would be kind of horrible, unless you merely want to have an idea of what colors are on the screen. crashboogie's two suggestions of acrylic layer cases and 3D printing are the two most likely courses to a workable solution. (A distant third, in terms of compact size and suitability for purpose, would be to get a "project box" of suitable size, cut a hole for the screen, mount the screen behind the hole, then mount the Pi to the back of the screen, then secure the battery somehow, then run wires in somehow - I wouldn't recommend that approach.)
For acrylic layer cases, Pimoroni has their Pibow PiTFT+
, which fits the 2.8" and 3.5" Adafruit PiTFT family of displays. And C4Labs.net has their Zebra Black Ice TOP HAT CASE
, which has extra layers to make it taller. Hmm, I think Pimoroni may have extra layers available for some of their cases too. But neither of these is likely to be exactly what you need, without some extra work.
My first case for my first Pi (a model B with an Adafruit 2.8" PiTFT) was a Pibow case; I wanted the front closed in a bit more, so I bought a small sheet of 1/16" thick clear plastic (polystyrene? polycarbonate? one of those), cut a rectangle the dimensions of the top layer of the Pibow stack, then with a bunch of drilling, sawing, filing, and sanding, I made a retangular hole that precisely matched the size and location of the active part of the screen (just the part with pixels), so it covered over the inactive border of the glass along the edges of the screen. Painted the inside surface of my newly made piece with black paint (formulated for plastic), and attached it using the same screws holding the layers of the case together. This resulted in a nice clean look (as long as you didn't get close enough to see my minor mistakes/scratches), and since only 90-ish% of the glass of the screen was visible (just the "working" part) and the rest was captive behind my front layer, it was quite secure. You may find a similar trick works for you. If you happen to know someone who can laser cut acrylic sheets, you could make a much prettier one than I did (then again, you could have them do a whole custom-sized layered case for you).
Anyway, look at the acrylic layer cases and if you don't see anything you can use or adapt, then I'd suggest browsing around on Thingiverse
- search for "Raspberry Pi" and/or the name of your screen and see what comes up. Somebody may have already designed the case of your dreams, or someone may have made something close and you can copy the plans and tweak it for what you need, then both sites can (themselves or by referral) help get it printed and shipped to you, if you don't know someone with a 3D printer.
One other approach, depending on your needs/uses, would be to find a tiny general purpose equipment case, like a Pelican 1050
(they have them in lots of different sizes
), and build your Pi/screen/battery into the case, such that the screen is secured inside the lid (facing in, when the case is closed), the Pi is in the bottom half of the case, attached to the screen via a several-inch GPIO ribbon cable, and the battery is underneath the Pi. In this case, you'd open the case to use it, like a tiny laptop minus the keyboard. It'd give you full access to the Pi for experimentation, with a sort of a hacker/steampunk feel. Not the way I'd go, but there were a bunch of folks doing this kind of thing a few years ago.
Oh, also, there is a Cases forum
on here on the site. It's definitely worth poking around in there too (but if you post the exact same question in there, the moderators may frown a bit - they prefer questions to live in just one place). Good luck in your search.