Usually, when a portal cannot be linked, there are two possibilities:
1) the portal is out of reach. This should not be the case, since, with the configuration you've showed, you would have had range problems only with L1 portals;
2) as you correctly said, there are fields and links in the way. It's impossible to cross two links, even if they are from your own faction. With the field configuration you've created, the only portals that can be linked to the Bird Library are these (one is under the word "resonators"):
Creating a link from these portals, if their level is high enough, should give you no problem. The rest is blocked by the field mantained by those two same portals. That's why, as a general rule, you should try to make your links the shortest possible: you always risk to block the creation of links/fields for you or your fellow agents.