Sounds like you may have several issues going on there.
There is a serial number break on the 480LL, that used two different types of brake acutuators. Prior to Ser. #16270319 are the same as on my 480C, so I can tell you a little about them, as I just worked on mine.
Poor brakes from the beginning could be a couple things. #1. Bad seals behind the brake housing. #2 Self adjusters on the brakes, not adjusting. #3 Wheel cylinder frozen up, and needs rebuilt/replaced. # 4 Master cylinder needs rebuilt/replaced.
On mine, the wheel cylinder, and master cylinder needed replaced. Also the parking brake band. The seals were good in mine, as the discs were dry. The wheel cylinder apparently seeped brake fluid, and got into the brake housing, and really corroded the brake band. Had it all froze up. I guess in a way I lucked out... Just a lot of cleaning up, replaced the brake band, wheel cylinder, and Master cylinder. I also went ahead and replaced the brake lines with alloy type lines, making my own.
If the wheel cylinder does need replaced, please make a mental note now... Be really careful removing the rubber line from the wheel cylinder. That little 8" hose is $48.00 from Case, and there are no after market ones...
The right pedeal going to the floor suggests to me, the wheel, or master cylinder needs replaced, or possibly just out of fluid. Have you checked them..?? They are located up under the dash, directly above the pedals. There is an access cover on top of the dash, on the left side, to see down into them. A long funnel is pretty well needed to fill them. Takes a 1" wrench to remove the cap, if it is an original.
If the wheel is locking up on it's own, without depressing the pedal, suggests to me, the external return spring is broken, allowing the brake to actuate itself. Locking, using the pedal, sounds like things are kinda' rusty/cruddy in the brake actuator. A good cleaning, and possibly needing new steel balls in the actuator. You can get them for about a buck a piece if you look.
On the bright side, if it is locking up, that would almost make me think, things are not oil soaked, from a leaking seal.
To see your brake mechanism, I've added this link. You may want to print this note, to see how to navigate the pages. Pretty simple, once you've accessed it as many times as I have..., LOL... I hope you have high speed internet...
Link to Case Construction:
CASE
In the top menu, put your cursor on "Parts and Service" A menu will appear below. Click on "search for parts"
In the next window, in yellow, it will say "Launch parts catalog". In the next window that appears, there is a place at the top left, to type in your model number, ie; 480LL. You will get one return in that list. 480 Construction King Loader. Below that, it will say "figure listing". Click on that, and it will give a complete listing of all parts, in an exploded view, by section. You'll want to check out sections 202 through about 232.
Get the serial number off your machine, before starting, so as you know what to look for.
A service manual for your machine is invaluable, and Case has some great ones, although pricey. I found one for my 480C on ebay. They also had copies on CD's for a lot less (About $40.00). Not sure of the quality..., so I got and OEM hardcopy, and has been well worth it to me. If by chance yours has the earlier version of the brakes, I'll help you as much as I can. Info, where I found aftermarket parts, most reasonable. I did a lot of checking, and these guys cannot be beat on prices. And..., I was lucky enough, that they are in the same state, and next day shipping wasn't needed... If I ordered before 10:00 or 11:00 am, it was at my door the next day.
One more bit of advice... It sounds like a lot of work, but it is much simpler to work on for an old guy like me, that doesn't bend like he used to, to remove the rear wheel, fender, and floor pan. That makes it wide open, and you are looking right down on it. You'll just need suitable blocking to hold it up. Again, I'm fortunate mine is a backhoe, and it is blocked up on the hoe frame.
If you do decide to remove these items, it is adviseable to have a helper when removing the fender bolts, at the floor pan. Those little caged nuts have a tendency to break their welds. Someone with a pair of vise-grips on the other side, would sure save a lot of time. Don't ask me how I know....
Hope this helps...!!