Searching within LinkedIn groups' members is limited to keywords only. If you search from within a group it may take a lot of time to sort out the results. However there is a way to do an advanced search within groups (one or more) and contact members - for free, without a paid account required.
Here is an example.
Looking for J2EE Engineers on LinkedIn (as an example).
1. Join all LinkedIn groups that are relevant. Search for groups in the group section by the keyword J2EE or Java or Software Development etc. and ask to join them. It may take a few days till you are accepted. Also, there's a limit for the number of pending memberships. But you'll get there.
2. It may make sense to edit your profile to reflect that you are looking for Java/J2EE Engineers, have Java openings etc.
3. When some of your group memberships are there. Go to the "search for people" page and press on the advance search TAB. Enter your search. As an example, enter "Developer" in the title and "Java" in the keywords. Below you will see the option to look in your groups (new!). Check all groups that apply. Go ahead and search (and sort by the keyword relevance).
You may want to try different searches, say play with titles and keywords, add a target company etc.
4. Go through the results. Click on profiles. Scroll the profile page down. On your right, you will see a "Send message" option. (Ignore the "contact" options that say Inmail etc. on your left, scroll down below that)
The "Send message" will be there, enabled, for the majority of profiles. This is because you are now members of the same group.
5. For each profile that seems appropriate click "send message" and send a message of your choice.