My car keeps having trouble going into 1st gear. I'll be at a stop light and it won't go in, and then I move the shifter right and left, and then it goes in. I have a Y80 5 speed transmission on an Integra. I don't know what exactly it could be but here are a few things I think may or may not be the problem:

1) My rubber floor mat might be too thick, so it is restricting the clutch pedal from going all the way in. I doubt this is the case because I have tried moving the mat back and even if I push the clutch as hard as I can, it still does it.

2) Transmission fluid might not be the problem because I just did a flush last season, and I have driven about 5000km on it only.

3) After installing my new short shifter, the shifter wasn't flush with the linkage, so it was making rattling noises. I added a couple of washers on either side of the shifter, and then bolted it to the linkage. It still makes the rattling noises because it's kind of loose. I need to fix the number of washers or get a new linkage. I don't know if this would prevent the transmission not going into 1st gear though.

Any suggestions?