Below is the snippet of the file, I need to comment out 2 line which runs MON-SAT and the script run_abcd.sh.

10 5-23/2 * * SUN . ~/.bash_profile; $HOME/scripts/run_abcd.sh > $DIR/logs/run_abcd.log
10 1-23/2 * * MON,TUE,WED,THU,FRI,SAT . ~/.bash_profile; $HOME/scripts/run_abcd.sh > $DIR/logs/run_abcd.log
10 1-23/2 * * MON,TUE,WED,THU,FRI,SAT . ~/.bash_profile; $HOME/scripts/run_deposit.sh > $DIR/logs/run_deposit.log

using below sed I can comment out the script run_abcd.sh but it comments out both line1 and line2. I need only second line to be commented. Please advise.
sed -e '/run_abcd.sh/ s/^#*/#/' -i file_name

That's easier under awk, but written in sed, you could add in a check. You are looking for lines with both strings, not just one or the others, so design your decision tree appropriately:

Also, only use the -i option with a value. That way a backup copy is kept automatically. The way you have it, a mistake will irreversably damage the orignal without leaving you an automatic backup.

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You need to comment out run_abcd.sh running Mon-Sat? If so, add Mon-Sat to the regular expression, for example

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