When I bought my Cannondale R1000 road bike I went through a lot of spokes. Over time I met a couple of folks and learned that they did too with the same bike. In that case the wheel manufacture had a run where they over tightened the spokes which led to several failures. I had to cut a century ride short because of a broken spoke and one the way back I broke two more, I was waiting for the wheel to completely fail that day (I got lucky).

I'm assuming you've had this bike for a while. In that case I would guess that the wheel got out of true over time, which put extra stress on the spokes and a couple of them broke. I imagine you are not riding it now, which would be good because the other spokes will break now that they are under more stress. You can replace the spokes yourself or take it into a shop. You can also check to see how true your other wheels are by simply spinning them and looking how consistently they run through the brake pads. It you see a wobble it might mean your spokes need adjusted.

If you want to fix it yourself this web site should help.

www.sheldonbrown.com/wheelbuild.html

It might look overwhelming so do a search for these two sections.
*Initial spoke adjustment
*Tensioning and truing

I wouldn't replace the spokes myself, I'd have a shop do it. The last time I was at the shop, I had them true both wheels, replace the tires and tubes, and replace a spoke, and it cost $80 for all of that. Shouldn't be that much to replace some spokes and true both wheels.

If you start braking spokes on a regular basis that wheel is probably cooked.

It the problem may not be that the manufacture had over torqued the spokes it may be that they put too much spoke prep on the spokes so they can't turn to start off with or there are times where alloy nipples will react to stainless steel spokes and began to bond to the spokes and can not turn. Either way the result is the same, a wheel that can not be trued.

Last but not leas the rim may be physically bent and no amount of "truing" can fix it.

Personally I am not a fan of factory built wheels because they are just cranked out of a machine from the far east and as a whole the quality control may be acceptable a lot of shops don't spend the time to true, dish, and adjust be bearings of a factory built wheel.

Please note, old Schwinns used steel rims and zinc spokes; probably the worst combination you can possibly build a wheel with.

If you have a name brand hub and it's in good working order you may be better off by having the hub being cut out of the wheel and relaced to a new rim using new spokes.

Since you are using a cruiser for basic transportation I would recommend having your local shop build you up a good new front wheel using a Surly hub and maybe a Sun RhynoLite rim. It will be pretty inexpensive and will probably outlast your bike.