Mod conflict is usually a safe bet. Or more likely, just an outdated one since you mentioned you patched the game. Make sure all your mods are compatible with the latest patch, or go through them one at a time until you find the one causing the problem.
I had the same problem with a toddler, and I haven't done any borking around with ages. I tried to age her with the birthday cake, and she got stuck in 'have birthday'. I eventually had to reset her, and although her picture showed a child, she remained a toddler. She finally aged on her own the next day (she should have aged on the day I tried to age her).
All I've got is Awesomemod, a hack that stops Sims from making those annoying choking sounds when they eat and a bunch of clothes, hairs and furniture. I just installed WA, Ambitions and LN and my game is fully patched, caches cleared, new town (Riverview) started after installing the EPs. I aged the same Sim to teenage with the birthday cake, and had no problems. Something is up - it sort of reminded me of the Sims2 problem wherein a baby wouldn't age if anything happened during the aging process.