I am not at all sure what your 'not on the input side' means. Please elaborate.
So, you have en electronic kit running into your PC, and have an Alesis I/026. Kewl.
IF I am understanding things correctly, you are having trouble when you try to trigger sounds in Battery.
It seems to me your ASIO Buffer Size is WAY WAY too high for recording purposes, and results in too much latency to ever be properly used for recording.
When I am recording, or just playing live using Sonar, I use an ASIO Buffer Size of 128. You need a latency of around 10 milliseconds or a little less to be able to play and record without noticeable lag.
On the other hand, once you are DONE with recording, and begin the mixing process, THEN you want your ASIO Buffer Size way high - perhaps up to 1024, to allow a large enough buffer for more robust effects (Perfect Space or Boost 11 are a couple), to do their thing. When mixing or mastering, you aren't worried about lag anymore.
Please try setting your ASIO Buffer Size down to 128, then cycling the audio interface, to reload the drivers in memory, and give it another shot.
Thanks,
Bob Bone