Open iTunes on your computer. Connect your device (iPad or whatever) to the computer. Hold both home and power buttons for exactly 10 seconds, release the power button, keep holding home button until your device recognises it is in Recovery Mode. (Perhaps 10-20 seconds.) If the device screen is black (blank) then it is in DFU Mode.
See this link and note the sentence commencing, 'If you restore from a different computer.... ' down near the bottom of the page.
Where have you been backing up to prior to your present difficulty? If it is not on the other PC that you have tried you will have to set it up as a new device on that PC and then switch back to the normal PC and do a Restore from the latest back up there (or from the I-cloud I you have been backing up there).
As for the device not being recognised in your normal computer -
Firstly, make sure that your device is not hidden (left hand pane). If it just reads device then toggle between SHOW and HIDE.
Secondly, try all the other ports on your computer, even a number of times.
Thirdly, if you have another computer try plugging your device into it without taking any action, give it a moment, remove it and try it back in your other computer again.
If you need further help on restoring from a previous backup just come back here!