You might try something called direct cable connect. This is something that you can Google and get many responses on how to do. It is a "free" program that Microsoft has provided. It might work where you have 98SE. I had Win98 first edition, and I never got it to work. (It can drive you crazy) You need to have the proper cable to do it, and there are many companies that will appear in the sponsored links who will sell one to you. Or go to your local Good Guys, Best Buy, PC store, etc. and you can probably get one a lot faster and might even get a good suggestion for accomplishing the transfer.
The previous suggestion about taking the hard drive from the old machine, changing its jumpers to make it a slave, and installing it in the new machine, is a good one. However, check inside your new PC first to make sure it has the appropriate connectors on the mother board. I tried doing the same thing when I got a new PC, but the old one was IDE technology and the new one was SATA, and never the twain shall meet.
I resorted to burning my old PC's files on a CD and loading them that way--not elegant, but it worked.