I understand that the bases are "floating" however, I didn't have a problem with this earlier so I'm not sure why its happening now. Also, if I can turn the H-Bridge on by touching the input pin to a 5V lead then I should have no issues at all with the H-Bridge itself. I don't follow the purpose of the 22kohm resistors, could you please explain?
It is just generally undesirable to have a control input at an unknown voltage. A base of a transistor that is virtually disconnected (in an open circuit state) can have its voltage level altered by noise, or people touching your circuit etc. This can lead to undesired or unpredictable circuit behaviour. So those resistors would help to ensure that the base of the transistor is always at a known (and suitable) voltage. Avoids false triggering, and prevents motors from starting etc when you didn't tell it to move. Look up info on 'pull-up' and 'pull-down' resistors. And look up issues with floating inputs.
For the moment, if your voltage supply is variable (eg. bench power supply), I guess you could see what happens if you drop your supply voltage down to say 8V DC..... and see what happens.
And look up the specs (data sheet) for the TIP32 transistor...... and see what base current is needed in order to make this transistor turn on properly for the amount of collector current that your motor needs to draw.
And when you mentioned that you had 'exactly the same circuit working earlier'..... are you absolutely sure that you're using exactly the same circuit? Obviously something has changed....or you changed something.