Wannabe triathlete can't swim

Welcome to the sport.  27 is young! 

Congratulations!  700 m breaststroke is pretty good, and doing that when you can only go 100 m front crawl says a lot. 

You wouldn't be the first to breastroke your way to a triathlon finish.  You'll find all types of strokes-- including "wading" if the water is shallow.  

L-E-S-S-O-N-S!!  Swimming is very technical, and since you're starting with the running/Cat3 cycling background with little natural buoyancy, get some lessons!  (Former lifeguard and swim instructor here.)  With little buoyancy, you're likely to experience "sinking legs" and this will be exaggerated if you're lifting your head even the slightest when you breathe.  I'll also suggest you probably need to slow down, especially at first.  I tell people they should swim like they're going for a walk in the park, not sprinting from light pole to light pole.  Additionally, relax!  When you're tense, you're working very hard against yourself.  What's common is for a new swimmer to thrash around trying to get to the far end as fast as possible.  They lift their head, splash a lot, and are generally worn out by the time they reach that 25 m goal!  They employ a "blast and gasp" style of breathing (blasting out the air they're holding in their lungs and gasping for another lungful of air before they commence "drowning" again.)  Imagine trying to do this while running?  

Slow down
Head position (look down at the bottom of the pool or even a little down your torso, water should hit your head above your forehead given your lack of buoyancy)
Rotate to breathe rather than lift your head.
Exhale slowly while your face is in the water and get a "sip" of air when you rotate.  If it helps, hum to exhale.
Kick!  Relaxed kicking originating at the hips to stabilize the torso will help keep your legs "flat" in the water.
Use your elbows.  Your arm should only be "straight" for an instant at the start of your pull and an instant at the end of the pull.  Elbow should be bent while in the air, bent SLIGHTLY when your hand enters the water, and bent during the pull (think of scraping your hand down your torso).  

When you're swimming slowly, you'll have to rotate a lot to get some air.  As you get faster, you'll create a little "trough" next to your head and won't need to rotate as much.  

1:40/100m is pretty fast!  Probably ~top 1/3.  The couple times I did coached lessons, I was able to do 100 YARDS on 1:40 intervals.  

Slow down!  You'll learn to relax more (and in fact, spend some portion of your "swim" time just playing around doing all the silly stunts 6 year olds do) and you won't *NEED* as much oxygen so you can PROVE to yourself that you've still got enough air to breathe in a more relaxed manner.  

Think of lifting your head as putting on the emergency brake!  As soon as you lift, your legs sink and instead of gliding across the water, you're plowing through it.  With your body and legs "flat" in the water, you can pass through an 18" circle.  Lift your head and your legs sink and now you'll barely pass through an 18x30" (or worse) ellipse.  That's 70% more water to move out of the way!  

There's a way to attach video, but I've never done it in posts.