Diabetic Neuropathy with Acute Onset: Given the patient's history of neuropathy, the acute onset of severe toe burning sensation could be an exacerbation of diabetic neuropathy, especially if the patient has diabetes. The discolored toes might suggest poor circulation, but good capillary refill makes this less likely as the primary cause.

Peripheral Artery Disease (PAD): Although the patient has good capillary refill, PAD could cause burning sensations in the toes, especially if the patient has a history of vascular disease. The discoloration could be due to decreased blood flow.
Chronic Venous Insufficiency: This condition can cause skin discoloration and pain in the legs and toes due to poor venous return. The burning sensation could be related to the venous stasis.
Vasculitis: Certain types of vasculitis, like Buerger's disease, can cause burning sensations and discoloration in the toes due to inflammation of the blood vessels.

Acute Limb Ischemia: Despite good capillary refill, this is a critical diagnosis to consider due to the potential for rapid progression to gangrene and the need for urgent intervention. The acute onset of severe pain and discoloration are red flags.
Deep Vein Thrombosis (DVT): Although less likely given the bilateral nature and the presence of good capillary refill, DVT can cause severe pain and should be considered, especially if there are risk factors such as recent immobility or cancer.
Sepsis: If the patient has an infection, sepsis could be a life-threatening condition causing the symptoms. The presence of neuropathy and potential for poor circulation might mask typical signs of infection.

Erythromelalgia: A rare disorder characterized by burning pain, heat, and redness in the hands and feet. It could be primary or secondary to another condition like myeloproliferative disorders.
Fabry Disease: A genetic disorder that can cause burning sensations in the hands and feet due to the accumulation of a particular type of fat in the body's cells.
Complex Regional Pain Syndrome (CRPS): A condition characterized by intense burning or aching pain in the hands or feet after an injury or trauma. It's less likely given the bilateral and acute onset nature of the symptoms but should be considered if other diagnoses are ruled out.