House has NO FLOOR JOISTS!?

You need to hire a contractor, and a building inspector would be a good idea too. Don't bring in the city inspector, you would risk having your house red tagged and you would have to move out until it was fixed. You should also contact your realtor to see if there was an inspection that missed details.

This is not an insurmountable problem, not by any stretch.

If the existing beam supporting the floor is in good shape, there's nothing stopping you from getting under the floor, carefully and slowly jacking it up until it is ever-so-very-slightly bowed UPWARD, and installing joists under the existing floor. Install a hanger on one beam, slide the new joist into that and get it tight up against the underside of the floor, and wrap a hanger around the other end and nail everything into place.

Lather, rinse and repeat every sixteen inches until the whole floor is done. Easy job.

You want to take it slow bowing the floor upward to avoid overstressing things above the floor and possibly causing cracks, and to give yourself just a bit of freedom so that when you let the jack off to lower the floor onto the new joist, everything settles back to perfectly level - or at least, less imperfectly level than it is.

Seriously. This is an easy job. Nothing difficult about it if you have access to the underside of the floor. It's only tedious.

Thanks for additional info. There are flooring systems that use 4ft x 2ft interlocking sandwich panels which is how your question reads.

What you describe sounds like a proprietary product from the 70s. This used to be a system that was popular for roof deck construction. The ones I used had two t's and g's and was called duo deck or some such, but others had single t's and g's. It spanned about 20 feet. It was a bit extravagant on timber but gave a soffit that didn't need much finishing but you had to be careful to keep it dry. Never seen it used for floors which is probably because it is not intended for higher loadings, and there are issues around fire protection, and running services through it. You might be able to rectify sagging by propping and joggling in additional beams mid-span or at at third intervals, depending how bad the sagging is. Sounds like you need an engineer on board to make sure you aren't throwing good money after bad.

Surely you did your own walk through? How is it this has only just been discovered? Anyway you don't need to 'gut the house'. You can do a room at a time. You can build sleeper walls or set large timbers on small piers to support new joists. I renewed a floor with honeycombed sleeper walls. DPC on top of the walls 4 x 2 on it's side (wall plate) and 4 x 2 joists. Use large screws diagonally through the joist into the wall plate. Top with flooring chipboard screwed intermittently. You can add insulation with foam sprung between the new joists. Do everything above standard such as slightly less joist centres and 22 mm chipboard. That way your floor will feel solid. Glue the tongues and grooves or the floor will squeak in use. Take your time to work out levels so that the surface ends up where you want it to be.

So what supports the flooring/subfloor between the beams and the outer walls? 2 X 4's? I remodeled an old 1900's era house one time that only had 2 X 6 ceiling joists and lathe/plaster ceilings that drooped over 2" in places from the weight of the plaster/lathe and time. Had to sister in new 2 X 8's for the room ceilings. Never seen 2 X 4's used for flooring/ joists.

The easiest solution would be to installed new 2 X 10 or 12" joists (depending on span) under the old flooring between the center beams and outer walls using joist hangers/straps to support the ends to the beams/wall plates...space new joists 16" apart on center. Home centers sell joist hangers in various styles and sizes. Just make sure the new joists fit tight under the existing flooring...may need to jack up flooring to get level as you go. You might also need to upgrade to 3/4" thick subflooring and properly done flooring.Might be best to call in qualified contractor/engineer/inspector to see what will be needed for new joists and to meet code for when it comes time to sell the house in the future.

if you can PROVE the inspector was a scam artist, the COMPANY he represents is responsible to you for potential damages that he did not disclose before you closed on the purchase.

What the heck is a floor joist? If the house was built it had to pass code inspections. You’re just being extra picky and should be happy you own a home.

Not sure there's any problem to worry about. It's unusual construction for a house, but not unheard of.

It sounds more like mobile home construction. U can rebuild it as desired. Paul H's scheme sounds like a n easy weekend ongoing project.

you brought the house without personally looking under the floors? ouch!

That said ... nothing is going to make those floors stop sagging without ripping up the whole thing and redoing it properly.

So asker is saying that his structure just uses some sort of plywood with flooring overelay and no other support . . . . . never seen anything like that: even a small closet floor usually has small joists under it.