Hello,
As i may understand, you want to get a list of websites linking to internal pages of your client's website (which are now borken 404). So, you can benefit from that link juice by doing some internal 301 redirects. Welll i have gone through such issues times before, and here are more tahn 1 way to get those links:
1. Google Webmaster Tools: This is the easiest one i think. Go to Google WMT ---> Traffic ---> links to your site ---> You will find a list of top linked pages at top left. (screenshot here: http://i.imgur.com/fFoLEJC.png). Click on "More" (i have it in french here: "plus"). You will geta list of the most popular pages in your site. Click on those pages 1 by 1, and u will get the external inbound links to that page.
2. Open site explorer from Moz.com here: Go fetch the inbound links to that domain, then click on the "top pages" tab. You will have a list with internal pages who received links and social share. Export this to a csv file. Then, take those urls 1 by 1 and fetch their inbound linsk using opensiteexplorer again. You will get a list of ddomains/pages linking to those internal pages 1 by 1 .
3. Use cognietive seo tools. They have a filter by url, so u can exclude hpage and llok for inbound links to remaing pages. But their index is limited (my own opinion)
4. Majestic seo tools: great index, easy-to-use filters so u may exclude hpage and lookup the rest.
Hope it helped.
regards