By 13 weeks your baby should be getting over colic; colic usually peaks between weeks six and seven and is gone by the end of month three - you should be just about there (my little girl had colic - she got fussy around noon, and from around 5 p.m. to 2 or 3 a.m. she cried and cried and cried and cried...; I barely remember the first three months of her life - she is now one of the happiest babies you'll ever meet, go figure).
First, have you taken her to the pediatrician to check for an ear infection? I have NEVER regretted taking my child to the pediatrician, even when she wasn't actually sick - the peace of mind - knowing that she's just fussy - was worth it! While you're there, you might also the Dr. to check for the gastrointestinal problems - acid reflux can be tough on a kid. If she's on formula, my ped. recommended Good Start - it's the easiest to digest and sometimes helps fussy babies.
If she's not sick... 13 weeks is tough in terms of entertainment, because they usually can't do much but are on the verge of doing so much more. And in the middle of the night, you aren't in the mood to put on a puppet show. In those circumstances, perhaps the best thing you can try are the various soothing techniques described in other responses. And, while I wasn't strong enough to do it, Dr.s have said that it's not too early to let her cry it out at night if you can. I tried it - it didn't work for me, but many parents swear by it.
Dealing with the boredom... I bought so many toys those weeks, and she couldn't use any of them! She did a few weeks later though, when she got the whole grasping thing. One thing I did to encourage her development was buy little hang-toys with chimes in them, so when she batted at them it made a pretty little "tinkle" sound, encouraging her to do it again. TinyLove makes this really cool hanging-link rabbit that I got at babies-r-us for around $5 or $6. At about four months (just a couple weeks away), my daughter really got into her exersaucer. Some babies also like a jumperoo.
The one thing you can count on - she will grow up and this will end!