How to plumb toilet drain?

I'm a pretty experienced remodler who recently installed a new low-flow toilet in a different location in my bathroom. Unfortunately, it doesn't flush. I suspect I've plumbed it incorrectly and hope someone can advise me. The old toilet was connected within 12" of a 4" drain/vent pipe and worked fine. I installed the new toilet 37" to the left of it's old location, installing a new closet connection and 4" PVC drain pipe with 1/4" drop per foot. This installation required turning the existing sanitary collar on the drain/vent pipe about 30 degrees and connecting a 4" drain pipe (37" in length) that connects to the closet flange. The installation went perfect until I tried to flush the new toilet (American Standard 2-piece gravity type). When I flush the toilet, the water raises in the bowl several inches, then slowly drops to the normal water level. If I hold the flush valve wide open until the tank drains completely, the toilet bowl will evacuate maybe twice in 10 flushes. I've double checked the drain pipe, vent pipe and toilet for obstructions and have none. I don't think the toilet is defective as I removed it and tested it on my patio - it flushes perfectly sitting on 4x4 blocks. I'm ready to pull my hair out over this---can anyone offfer any advise. Thank you

pipe

From your description there is nothing that should cause that problem, as long as you did not install a "P" trap under the floor. Therefore, the most obvious reason, without being there to check it, would be something caught in the new pipe obstructing it.

I've actually had the toilet off twice and even replaced the 4" PVC pipe (again) increasing the drop-per-foot in the drain pipe from 1/8" to 1/4" per foot. I'm begining to suspect a closet flange angle problem. All toilets I've seen have the closet flange pointed directly away from the rear of the toilet. My closet flange and drain pipe are turned about 30 degrees. Do you know if that may impact the flush?

drain

It has nothing to do with it. I routinely turn them up to 180 degrees depending on where the best location is for the vent pipe to rise in a wall. It is not a pitch/slope problem either as long as it is at least level.