The answer came thanks to @hnkotnis at xda-developers.com and his info (and experience) on how to get into "Download Mode" without seeing the screen.
My review of what I did to get Heimdall connected without root, debug mode, and a screen/lcd to see:
First, I am on linux (debian) so no Odin, I used Heimdall and Heimdall Frontend:
* disconnect USB
* pull battery
* let set for a minute
* Press HOME+Power+VolDown for 2 seconds beyond the vibrate (total of about 5 seconds)
* wait 3-4 seconds
* press the VolUp button
* plug usb in
* press "Detect" in Heimdall Frontend
You should get a "Device detected" in heimdall frontend. I also noticed a difference when connecting the usb cable with in "Download Mode" versus not in Download Mode.
Normal USB Connection
Jan 28 10:29:13 xia kernel: [1119572.140189] usb 5-8.3: new high-speed USB device number 31 using ehci-pci
Jan 28 10:29:13 xia kernel: [1119572.233321] usb 5-8.3: New USB device found, idVendor=04e8, idProduct=6865
Jan 28 10:29:13 xia kernel: [1119572.233332] usb 5-8.3: New USB device strings: Mfr=2, Product=3, SerialNumber=4
Jan 28 10:29:13 xia kernel: [1119572.233338] usb 5-8.3: Product: SAMSUNG_Android_SGH-T999
Jan 28 10:29:13 xia kernel: [1119572.233343] usb 5-8.3: Manufacturer: SAMSUNG
Jan 28 10:29:13 xia kernel: [1119572.233349] usb 5-8.3: SerialNumber: e70a909e
USB Connection when in "Download Mode"
Jan 28 10:30:18 xia kernel: [1119637.932207] usb 5-8.3: new high-speed USB device number 32 using ehci-pci
Jan 28 10:30:18 xia kernel: [1119638.024825] usb 5-8.3: New USB device found, idVendor=04e8, idProduct=685d
Jan 28 10:30:18 xia kernel: [1119638.024834] usb 5-8.3: New USB device strings: Mfr=1, Product=2, SerialNumber=0
Jan 28 10:30:18 xia kernel: [1119638.024840] usb 5-8.3: Product: MSM8960
Jan 28 10:30:18 xia kernel: [1119638.024845] usb 5-8.3: Manufacturer: Sasmsung
Jan 28 10:30:19 xia kernel: [1119638.113455] cdc_acm 5-8.3:1.0: This device cannot do calls on its own. It is not a modem.
Jan 28 10:30:19 xia kernel: [1119638.113598] cdc_acm 5-8.3:1.0: ttyACM0: USB ACM device
Jan 28 10:30:19 xia kernel: [1119638.114388] usbcore: registered new interface driver cdc_acm
Jan 28 10:30:19 xia kernel: [1119638.114391] cdc_acm: USB Abstract Control Model driver for USB modems and ISDN adapters
You can see the thread on the xda forum here: http://forum.xda-developers.com/showthread.php?p=49840347