You do not need to hold down he home button to get the power off slider. The power button alone will do the job. After powering back up, this will fix most problems.
The two button combination is for a reset, and you would hold it down for about 7 seconds, or better yet until the Apple logo appears. Ignore the power sider if it appears. The iPad will reboot without any further input. Normally you only do this when the iPad is frozen, or a normal restart does not work.