T41 damages battery / very fast battery wear

[jullass]

I have problem with batteries in my T41 laptop.
I bought it used, with a totally worn out battery (holding about 10 min).

I bought a replacement battery (9-cell, a cheap replacement one). The new battery held for about 5-6 hours in its first few cycles... but then the capacity began to drop dramatically - about 5% "last full capacity" in /proc/acpi/battery/BAT0/info every cycle. After just four months and just *17* (!!!) cycles (as noted by the original battery monitor on Windows) the "last full capacity" fell from around 70000 mWh to 4000 mWh and the battery held for about 20 minutes! I am now trying to get refund from the shop I bought it in, but they refuse me claiming that the producer has sent back the examined battery stating that "it's been used improperly" (they don't tell me any more detail).
Okay, the laptop was used mostly on AC power; most of battery uses were down from 100% to 50-60%, and back on AC so maybe it weren't the healthiest conditions for a battery... but I think that no new battery should go dead in 4 months, no matter how badly treated! The funny part is, that the monitor on Windows shows "Wear level: 0%".

But now I bought another battery. I didn't trust cheap replacements anymore so I bought an original IBM battery. An used one. Having gone through 107 cycles, the battery "last full capacity" was 43700 mWh, out of "design capacity" 47510 mWh, and it was described as "in good condition" by the monitor in Windows.
I have the battery for a week and I have used it two times for now - each time going down from 100% to around 5%... and the same thing happens that happened with the old battery. After the first discharge-charge the "last full capacity" fell to 40500 mWh. After the second one - to 38220 mWh! It's insane! The battery has lost more capacity in the last 2 cycles than it had had in the previous 107 ones!

As it's the second battery in this laptop that behaves this way, I ask what other thing than the battery itself can cause this behaviour? I thought that the electronics inside the battery is solely responsible for the charging/discharging.
Can some software affect the way battery is charged/discharged and cause damage (I run Linux)? Can the AC adapter be a problem (I've had this problem both on an original IBM adapter and a replacement adapter)? Or is there anything else in the hardware that could cause my T41 to make batteries wear so fast?