After some effort I was able to get this to work. I am surprised that much of the documentation (spartan 3 starter kit, USB 2 Module, Adept documentation) was not very clear on this process atleast for this old board/software combination.
I was able to get this working through opensuse 15.x and same should work for other linux distros as well. I also tested this in windows xp with Adept 1.x version and it works.
S3 board
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Connect the Digilent USB2 module to A1 expansion connector
Put a jumper in jtag connector to bypass cable. This is indicated in the board.
Put a jumper to middle pins of J8
Remove all jumpers from JP1
Software
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Install adept-2 using RPM or Debian package. Adept link - https://reference.digilentinc.com/software/adept/start. I used latest versions of runtime and utilities. In my case RPM package installed without any issues for both utils and runtime. Read the read me in each package if this fails.
Install dependencies specified in readme's of above packages. Most importantly libusb.
Perhaps you will have to reboot the machine after these steps.
After these connect the board and issue djtgcfg enum and device should be listed. This was my result:
Device:
Device Transport Type: 00010001 (USB)
Product Name: DModUsb1 V0.0
User Name:
Serial Number: 10054d008790
Note that there is no name for the device in the above output. (No text after Device:). If there is a name already skip the next step.
Add the device to the table using dadutil as follows. In my case I gave the device the name 's3'. Replace serial number as required.
dadutil tbladd --alias s3 --conn SN:10054d008790 --dtp USB
Initialize the jtag chain.
djtgcfg init -d s3
Create your bit file using xilinx ISE. Make sure to setup the FPGA startup clock to JTAG clock in property window of 'Generate Programming file' process in ISE
Program the FPGA with the bit file as follows. In my case FPGA had the index '0' in jtag chain.
djtgcfg prog -d s3 -i 0 -f <bit file>
If you are using windows XP use adept version 1.10 as 2.x did not start in XP. In XP, adding the device to table was automatic however.