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I'm not familiar with this device, but can you still get into TWRP? If so, try a different ROM to see if you can get it working again. Of course you really should have used TWRP to make a backup before you tried flashing anything: if you did that you'd be able to just restore the ROM from the backup (first rule of root club: always take a nandroid backup before modifying the system software in any way).
But what bothers me is the fact that you can't get into download mode. Because on any device I am familiar with a ROM flash should not do anything to that. So I'm wondering whether you used a ROM for the wrong model of the S4, or maybe a TWRP that was built for a different model? I'd be tempted to reflash to stock, but I think you need to get to download mode to do that (as I say, not a Samsung expert).
BTW the wipes you do before flashing a ROM (data and cache) won't remove the previous ROM. You do not need to wipe system (the ROM) or boot (kernel) in order to flash a ROM.
Open cmd, cd or drag the adb files into cmd. Adb reboot download will bring you back to download mode, as long as the drivers are correct.
If you can boot twrp you can flash a custom rom. If it'll only go into download mode you would need to flash stock firmware.Can i flash ANY rom from download mode or does it have to be the stock samsung firmware.
keep in mind that the rom needs to be created for your phone.....so no not ANY rom.Can i flash ANY rom from download mode or does it have to be the stock samsung firmware.