The most famous manufacturer of computer processors is IBM. The most famous manufacturer of computer processors after IBM is AMD.
IBM does not make laptops. IBM makes processors that are used in computers, but not actual computers. So the answer to your question would have to be Dell.
Apple worked with IBM and Motorola to develop the Power PC processors which were a development of IBM's POWER1 processor. Apple used Power PC processors in their range of Macintosh computers between 1994 and 2006 when Apple switched to using the processors from Intel's range. IBM produces a range of processors for all types of devices including the Cell processor used in Sony's PlayStation (The X Box also uses a Power PC processor). (See links below) In 2008 Apple spent $278 million to acquire PA Semi a company which designs processors based on the Power PC model. It is not known what Apple intends to do with processors designed by the company.
This is a bit of a confusing question. IBM-Compatible computers are a type of microcomputer themselves. Any x86 based processor, such as AMD, Intel, VIA, and Cyrix, are IBM-Compatible. Other systems also exist, such as older Macs which used IBM PowerPC processors and Motorola processors. There also exists Sun Systems SPARC processors, and a whole host of others. IBM-Compatibles are the current dominant consumer system.
IBM AIX currently only supports Power chip processors, which are not the Intel X86 format.
MS-DOS
Intel is a brand of processors and PowerPc is made by IBM
No version of Windows runs on Motorola-designed processors. Certain versions of Windows NT and Windows CE ran on PowerPC processors, which Motorola manufactured along with IBM.
Almost all can, indirectly by using logic or code tricks. However some processors, such as the POWER6 and POWER7 processors from IBM, can actually process in true binary.
Prior to switching to the Intel processors Apple used the PowerPC (PPC) processors. They were developed by Apple, IBM and Motorola (the AIM alliance) with most of the manufacturing done by Motorola (IBM produced the 64bit G5) until they pulled out of directly manufacturing in 2004 with Freescale Semiconductor taking over the manufacturing.
IBM was developing Cell processors for the PS3 and cancelled the line.
Neither one is a particular computer (they are manufacturers, not model names), and neither has a product lineup solely compatible or incompatible with Windows 98. IBM made several workstations with PowerPC processors that obviously cannot run Windows 98, and newer Macs have Intel processors that can run Windows 98, though the hardware is not fully compatible.