Sent emails asking for letters of recommendation, but no responses/agreement to write letter
They are probably just very busy. Try to ask in person if at all possible, since emails just get lost in inboxes.

Also, the referee may not feel they have the time to write a reference, since there can be a substantial upfront cost in time just to figure out what needs to be said. You can help them, and you, by providing a draft of a reference that contains the main things you think should be said. This sounds a bit cheeky, but can be very effective at cutting the perceived effort in writing your reference, and thus improving the chances they'll agree to provide one.