Given the information provided:

AFP (Alpha-Fetoprotein) is 1700: This is significantly elevated, suggesting a possible germ cell tumor or hepatocellular carcinoma.
CEA (Carcinoembryonic Antigen) is 6.1: Slightly elevated, which can be seen in various cancers but is not specific.
CA 19.9 is normal: This marker is often elevated in pancreatic cancer, but its normal level here makes pancreatic cancer less likely.
PET scan shows a tumor on the liver: Indicates a primary or metastatic liver tumor.

Hepatocellular Carcinoma (HCC): The significantly elevated AFP level, in combination with a liver tumor on PET scan, strongly suggests HCC, especially in the context of chronic liver disease or other risk factors not mentioned here.

Metastatic Liver Disease from a Non-Hepatocellular Primary: Although AFP is elevated, it's not exclusive to HCC. Other cancers can metastasize to the liver and cause an elevation in AFP, though this is less common.
Intrahepatic Cholangiocarcinoma: Though less likely given the normal CA 19.9, it cannot be entirely ruled out without further investigation, as some intrahepatic cholangiocarcinomas may not elevate CA 19.9.

Germ Cell Tumor with Liver Metastasis: Although rare, germ cell tumors (like yolk sac tumors) can present with very high AFP levels. Missing this diagnosis could be critical due to its potential for cure with appropriate treatment.
Pancreatic Cancer with Unusual Marker Profile: Although CA 19.9 is normal, pancreatic cancer can occasionally present with elevated AFP, especially in the context of a tumor with neuroendocrine differentiation or other rare subtypes.

Hepatoblastoma: A rare liver cancer that typically affects children but can occur in adults, often presenting with elevated AFP.
Other Rare Liver Tumors: Such as fibrolamellar hepatocellular carcinoma or epithelioid hemangioendothelioma, which might not fit the typical marker profile but could be considered in the differential diagnosis based on imaging and clinical presentation.