If the bike is comfortable and you can get where you want at an acceptable speed, I would just slap some slicks on and fix up your current bike, but I'm also a cheap-o.
But since talking about bikes is fun, if you do decide to get a new bike, consider what kind of riding you may use it for outside of commuting. I opted for a used craigslist touring bike; touring frames are generally touted as a good option for commuters since they are a road-style bikes that are generally meant to be comfortable for long hours in the saddle and rugged. I went with this option because it's good for commuting, and I planned on doing some touring later. If you're interested in cyclocross or mountain biking or road racing at a later time, consider getting one of those, etc.
Pretty much any bike is suited to commuting. Consider what your priorities are: Do you want to get there fast? Load the bike with all your stuff? How much maintenance are you wanting to put in? Reliability? Comfort?; and act accordingly. Also consider if you'll want a rack and panniers, backpack, or if you're going to just store everything at work and carry nothing (except emergency stuff).
Again, I'm a fan of touring bikes, but you've got lots of options, and pretty much anything will work, probably including what you've got.