Thank you again for your help, its nice to see these old forums still have active members that are very friendly and willing to help.
Thanks. I've been here over 20 years. Just an old guy watching over an old forum.
There are so many things that could be causing your problem. My sled sat for years while I was busy with other things. After I retired, I had time to try to get it running again. I could only get it to stay running with the choke half on. Dragged it in the barn and cleaned the carbs. There is a nice step-by-step with pictures in the tech section. I changed the fuel lines from the fuel pumps to the carbs because they were all brittle. That can cause cracks in the lines and suck air. Vmax-4's have a special fuel filter in the tank. It's a single filter with 2 nipples for the 2 fuel lines that come out of the top of the tank, and they're very hard to find. I drained the tank, installed my last one, mixed some premium gas with 100 octane race fuel, and started it up. It was still acting like it was starving for fuel, so I took it all back apart and took the floats out of the carbs. I cleaned the needle valve filter. That was not in the tech write-up. There was some crud floating around where the fuel comes in to the carbs. It ran very well after that. I always mix some Yamalube with the gas at the beginning of the season until I see the oil level in the oil tank going down.
It is recommended to run your sled with the air boxes on. Once you get it running like it should, you might want to put them back on. While you've got them off, take them apart and look at the white nylon collars where the rubber carb boots attach. They're called pipes and are part #19 on the Air Cleaner page in the service manual. They have white tabs that can get brittle and break off and get sucked into the engine and cause catastrophic damage. If any are missing, or pieces broken off, check your reed valves to see if there are any pieces stuck in them and get them out! Use the search feature at the top of this or any page on the forum and search "white tabs". It is a common problem that has ruined many engines.
https://vmax4.com/threads/white-tabs-watch-out.11604/
As far as the filter foam material, check this out:
https://vmax4.com/threads/possible-fuel-filter-issues.33244/#post-114887
This might be a longshot, but if your sled has been sitting a long time, you could have mice or a mouse nest in the exhaust. They like to drag insulation, string, corn, etc. into that hole they see coming out of the bottom of the hood and make new homes. That could restrict the airflow coming out.
The Search feature at the top right of any page on the forum is a good tool. There is a lot of information here, and any problem you may run across has more than likely been discussed before. I don't think you will find more information anywhere else on the web.
That should keep you busy for a little while. Post back here and let us know what you find.
Shark