I have a 2001 corolla and I was just rolling into a driveway which is actually a lawn with some snow on it in my neighbourhood. Anyway, today the weather was milder and 3-4 inches of snow was wet and heavy. Turning into the spot, about half a carlength in, you could feel a little stress on the power steering. From there, the car moved straight for about a foot and the steering wheel wasn't completely straight. From this moment on, the engine was significantly louder. No clicks/clanks/whirrs, but just the engine was louder. The dashboard was vibrating and so was my steering wheel.
I knew something was up so I didn't even wait until tomorrow. I pulled out and took it for a test drive down the street and around the block. Making very sharp turns, like in a parking lot, the vibration was louder. Also, at certain RPMs, the car was louder. I was worried it was a transmission thing, but the car seems to be switching gears pretty easily - just with noise. I got up to around 80KPH and it was almost as if the noise was gone (but it was still there and noticeable). Accelerating, from like gear 1-2, 2-3 for example, is accompanied by a significantly louder engine.
At first I thought with the snow and budget driveway, maybe the wheel was shifted or something? However, after that test drive, it appears to be an engine noise.
Any advice would help + let me know any tests you want me to try.
additional details from today's drive to work: When going in reverse, the noise/vibrations are almost gone. Noise occurs when in park/drive. Also, vibration/noise is very prominent when going from complete rest to drive ie. Start to drive when traffic light goes from red to green, after stop signs, etc.