Just to reiterate some things you may not have gotten out of the previous posts, along with more detail in some cases, to help you get your system working. After that, some thoughts on your most recent test results as they relate to your previous test results, clarifications of some information you might only know part of, and suggestion as to course of action at this point.
Apologies for the length; I put it all here in the hope it will be useful.
If the controller and display don't come as a set, they may not work together regardless of what brand/model/maker/etc they are. (they might, they might not, it's just about a crapshoot).
If you don't go thru all the settings in all the display menus and make sure they are correct for your setup, the system may not work as expected even if they come as a pair. If there are no menus, no user-setup at all, then you can't change anything in the system, not even the wheel size, and so the speedometer wouldn't be very usable since it might be factory set for the wrong size wheel. Etc.
If the display is blank, and you cannot use the steps in the manual to get into the menus to set it up, then you have hardware troubleshooting to perform. Possible causes include:
--controller and display are incompatible with each other
--one or the other of them has a problem
--there is a connection failure between them
--there is a miswire between them (pin order on connectors is different between the two)
--battery power is not reaching the display correctly (unlikely since the controller does work after a delay, and it could not if battery power didn't reach the display to then power on the controller)
Etc.
Assuming anything when troubleshooting is generally unhelpful; testing each possible thing that could be wrong, step by step, and noting down each test peformed along with each result to eliminate them is generally helpful. Troubleshooting is a process, and if followed logically, including noting down each test done and it's results, will eventually find and fix problems.
Firmware and the software to install it is generally not available except at the factory.
(The only real exception is open-source firmware OSF OSFW written by end-users for specific models and versions of specific displays and controllers (see the various threads on those here on ES for what the OSFW does that the OEM FW doesn't, and what you would have to buy to be compatible with each particular OSFW, if interested)).
Since the system does power on and operate eventually, but runs slowly, it implies that the controller is running in a limited default assist mode it starts up in if it can't talk to the display, or receives invalid info from the display telling it what mode to be in.
If the original display was blank, but the system still turned on and operated, it probably means the display unit had failed, but the rest of the system was still working. If this isn't the case, then you would need to be step-by-step-clear about the exact problem sequence you originally had that led to the blank display.
If that *is* the case, then your original controller works fine, and it's just your original display that failed.
Since the new controller has, from what little info has been provided so far, never worked correctly, I would put the old one back on, and order a display identical to the original display, so that you have the best chance of it being compatible.
The new controller being "similar" to the old one but not identical makes it pretty likely that it is not compatible with the original display (and thus the new controller wouldn't be compatible with a display that *was* compatible with the old controller), and if the display was not bought with the controller it is pretty likely that it is not compatible with it either.
If you get a display that is different than the one specifically meant for that specific controller, there is a good chance it won't work. It doesn't matter if it is for the same company (bafang)--bafang makes a lot of different systems that are NOT inter-compatible. Just because it says bafang on it doens't mean it works together.
(if you are curious, look thru my posts a few years back about a "bafang" fatbike motor wheel kit I tested, the display for it doesn't work correctly on a different controller of the very same type and brand as the one with the kit, and the display from that different controller also doesn't work correclty on the kit's controller--even though both displays are visually the same and both controllers are the same brand).
Your motor manufacturer has nothing to do with whether a display (or controller) with the same brand name on it will work with each other. The only thing that matters for that is if the *display* and *controller* are matched with each other. The motor will generally work with "any" common brushless ebike/scooter/etc controller, as long as the connections to it are the same, or you wire it to be the same.
All ebike parts are "Foreign"; virtually every single one is made in China, regardless of what a seller may tell you or what sticker they put on it that says differently. Virtually no seller does anything at all to what they buy from China; the very few that do may put a sticker on it with their brand (if they didn't just have the factory or a warehouse in China do that for them); maybe less than a handful might actually do some form of testing to verify a few of their products as random sample testing. So if all foreign parts are suspect, then all ebike/scooter/etc parts are suspect, no matter where they are sold from.
There are exceptions to every rule, including this one.
Personally, I don't like fixing things. I like building something and having it "just work" and stay working.
But stuff doesn't ever seem to work that way, and it costs too much to have other people fix things for me, so I learned the process of troubleshooting and got pretty good at it. It's tedious, time-consuming, and brain-melting on occasion...but when used methodically, it works.