You have several problems, no matter how old the games are You're trying to play ...
1st) The celeron processor is the cheapest and weakest of the processors except for the Via processors of the same time period. Those days really were the best tmes for AMD. You'd prefer at least a Pentium II (2), and Your motherboard should support up to a 600+Mhz chip roughly. Either could be found for under $15.00.
2nd) The amount of RAM in the system is under what WinME likes to play with. You should have at least 256Megs for WinME, and it will handle up to 512Megs.
3rd) The fact that You have "a lot" of hard drive space running under WinME. WinME only supports a hard drive partition of 20Gigs maximum, and it requires it to be a FAT32 formatted partition. Anything over 20gigs will not be recognizable by Windows, and files or info stored there will cause errors. Especially video swap (temp) files trying to use FAT32.
Last) Although I love WinME myself for all my old DOS days games, I now use it as a Virtual machine under WinXP Pro. this allows me to still access all my old software and forms and fancy paperwork I did back in those days without losing either the hardware or storage benefits of XP Pro.
Although Your system (barely) meets the requirements for XP Home without any service pack updates, I'd highly recommend plopping down a simple $65.00 plus shipping into a 2.4Ghz barebones and swapping the larger hard drive into it. And backing any files from the actual (used by WinME) 20Gigs onto a $6.00 flashdrive for use under XP/VMachine or onto CDR/DVDRs.
As far as fnding a copy of Win98 or 2000, don't bother Win2000 was dropped within a year of production for support, and most hobby users don't even touch it - while stuff for 98/ME can still be custom written and found on some archives sites.
You'll find such an enormous improvement in the games that you probably won't want to swap Your $55.00+ gaming graphics card into the new system either.
www.geeks.com www.newegg.com www.retrobox.com
http://www.geeks.com/products.asp?cat=SYS
Good Luck!.