Don't give up
tl;dr
If you are still having trouble with restoring the phone with both Heimdall and Odin I would suggest trying the same from another computer.
OR
I went through a similar situation last month with my cappy after recently resurrecting it. It had been softbricked since back in the summer and I resurrected it using Odin under Win 7 on my laptop in January.
Subsequently I had an experience similar to Asher's regarding not getting past the at&t world phone image. From that, like Ashar Majeed, I was getting a black screen and not even a boot image, for a short period I could not get it into either download or recovery modes. . Searching led me to the same thread referenced earlier by BWolf56 (?) regarding getting into download and recovery modes. It took a number of attempts with several of the methods but I eventually was able to get into download mode.
By this time I no longer had Windows on any of my computers and attempted using Heimdall on a Linux install on the same laptop. I used the UCK44 Heimdall Oneclick and it would stop at varying points, most commonly at the kernel. I then tried using the full Heimdall after decompressing the .tar file and had the same poor results. I came to the same conclusion mentioned on a previous post in this thread. I thought my internal SD was bad.
Before throwing the phone in the trash I changed to my Linux desktop and was able to use the same Oneclick file to successfully restore my cappy. I used the same download of the oneclick, I transferred it to the desktop from the laptop with a thumb drive, so I don't think the laptop grief was due to a bad download of the ROM. Also, like Ashar, I no longer receive an indication that the phone is charging when the screen is off. There is no "star" when the phone is off nor a battery when the phone is in sleep mode.
The phone has been running well as a media device and navigation device for the past several weeks. I am using it with no sim card and leave it in flight mode when not using the GPS. So, don't give up on your cappy, it may still be serviceable.