Wont run below 4000rpm. Bike had been standing for several years new battery, oil changed ran fine initially but took out for a shakedown run today. lost power on a motorway (freeway) section like it was running out of fuel. If spin over a while on starter or bump start will fire up and revs fine but wont run low down below 4000rpm seems to go on 1 cylinder then dies. keep it revving and it pulls ok all fresh fuel pump runs fine all other electrics working ok

I had this problem today with my bike and after much ado I discovered there was oil in the air filter box... check your oil level it could be too full. Mines was and the excess oil was blown into the air filter box and as a result contaminated the air filter. Spent today cleaning the filter box, carb and draining and changing oil, could not get a new air filter today so ran it without onebike runs like new!! New air filter will be here Monday!

Might be a faulty side stand lockout switch. They're subject to a lot of wear, tear and grime and tend to wear out. So your bike thinks the side stand is down when it isn't locking your bike out so it won't start. Failing that it may be a faulty neutral switch, again the bike doesn't know it is in neutral so doesn't start.
I am going to state the obvious also, is your main kill switch turned on?

http://www.bikebandit.com/houseofmotorcycles/1999-honda-vfr800fi-interceptor/o/m2796#sch106813

here is a diagram showing the side stand switch. you can use a jumper wire at the eletrical connector to verifly the switch is bad. Or use a VOM to check for continuity.

Check your CDI on the other bike is a good option. if it was perfect before the CDI change then the new CDI is the only variable.
Wont be shimming.the valves need to wear to change that setting, and the bike has been sitting.
Sounds like its sucking air after the carby once over, but the balancing would have picked that up.
But how did you balance them if its idling at 5000rpm?
Recheck the carb once over,and balance, and make sure the fuel and vacumn tubes are in correct positions. check the throttle cable is replaced correctly
I assume it is running on all cylnders.

short pipe shouldn't cause you any problem...if it starts to backfire a lot after coming down from high speeds then you might want to think about installing something with a little more back pressure. #2 you"ll know it needs an oil change by if it smells burnt, has a slight fuel smell, or it looks real dark black. Now never ever top off your engine oil, pour only 2 and 1/2 bottles at first, start engine let oil get into the filter now shut off, pour a little more in, fill up to 3/4 either on site glass or using a dip stick, and if it uses a dip stick dont screw it in, just drop it in to measure. also check the chain for wear and stretch....you"ll know its stretched buy purchasing a pit bull type rear wheel stand which is a must..you'll always be using it...and spin the tire and check several spots on the bottom of the chain...if some portions are tighter than others then its been streched and now your riding on borrowed time. I"ve had three chains on my bike in a year and a half. Now im gonna need some sprockets next. #3 try to push start the bike to get it started then if it does start ride it somewhere where you can run it for a good solid 15-20 minutes to charge up the battery. if thats all it was, then your battery is probably old and will need replacing..avg bat life is two years! batteries can be expensive, i bought a Yuasa $95 about a year ago and working fine.Hope you found all this info very helpful.

starter solenoid sounds like it jamming knock itaround and

Since it ran fine before you "fixed" it, go back over the things you changed. Put the old spark plugs back in it. Double check all spark plug wires and ignition connections. Put the bike in a dark area and run it at night, can you see any arcing anywhere?

the problem is your fuel pump check the connection if it is ok then you must change it.

The issue I had with my 94 was due to an oil adjustment, wich you can find below the carbs. It ran great at full throttle but once it sat at idle, the plugs would get wet and the same type of bog would accure. Get new plungs and make sure all three are firing first, if they are then the oil adjustment is off. If not sorry to say but you may have a bad coil.