Not sure this'll work, but...
One way to test is to Safe Boot from the HD, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, Test for problem in Safe Mode...
PS. Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive
Reboot, test again.
Check in System Preferences > Universal Access > Keyboard, and make sure that neither Sticky Keys nor Slow Keys has been enabled.
Also, in System Preferences > Universal Access > Mouse, make sure that Mouse Keys has not been engaged.
One other possibility, perhaps. Since you have a wired keyboard, it probably has a built-in keypad. Make sure that NumLock has not been turned on - it can cause odd keyboard responses. To turn it on/off, hold down Shift and press the Clear key in the keypad (that's the key immediately above the 7 key).
Can you type normally if you physically take out the battery, let the laptop rest without the battery for a little while and then power up with only the adapter and cable, without the battery?
If so, you may have a swelling, bulging Apple battery that is exerting upward pressure n the trackpad.
Very common with certain kinds of Apple laptop batteries.
Replace it with a generic battery from amazon.com—not with the overpriced (and prone to bulging) Apple battery.