I do not use the Sony software, but perhaps I can help. It really sounds like you should just start over. In other words remove all books from the reader, then put the ones you want on there back on. Then it should sync fine again on the new computer. I would not try to sync again on the old one, as i can "confuse" them....
Hope that helps.
Welcome to the forum aeiouna. Be sure and check out all the free books here at mobileread
https://www.mobileread.com/forums/forumdisplay.php?f=126 that are ready to go for your Sony. You can also look a few forums down from that one and get many ePub books that will also work..... And here is a like to free ebooks from the Sony store
http://ebooks.addall.com/sonyfree.html . Be sure to check back on the Sony link as the book content changes. Also Kobo is a great sight for buying books
http://www.kobobooks.com/ and is often cheaper than the Sony site.