I am trying to use this command to find out the occurrence of the service "Loadservice" from the log file "log.06102010.svr1" in between the time frame 02:00:00 to 03:00:00 on the day 06-10-2010.
sed doesn't work that way. If you don't have a line EXACTLY matching 2010-06-10 02:00:00, it will never begin, and if you don't have a line EXACTLY matching 2010-06-10 03:00:00 it will never end.
Also, word count probably isn't what you're looking for, but the number of lines containing that word.
You can probably do it with awk, but we will need to see what your logfile looks like.
The first command in your pipe should open the file; the second command should default to its stdin (that reads from the pipe).
But perhaps can be boiled down to one sed command
sed -n '/2010-06-10 02:/,/2010-06-10 03:/{/Loadservice/p;}' log.06102013.svr1
Still it needs to find at least one 02: and one 03: entry in the file.
It is identical with
sed '/2010-06-10 02:/,/2010-06-10 03:/!d;/Loadservice/!d' log.06102013.svr1
Yes, that's the hour and its count.
The awk looks for lines that contain the target date AND the search word "LoadService". If found, a counter array indexed by the hour (two digits from time string) is incremented. In the end, the result is printed.
The nice thing about dates in YYYY-MM-DD HH:MM:SS order is they compare alphabetically. An exact match is no longer necessary -- you can use >, >=, <, <= to compare the date and get logical answers. awk will take one or more files, too.