That's a tough call - as old as the system is - and without a PCI-e slot to upgrade the video card - I can see where swapping the MOBO might be an option but even with that the CPU - Low amount of Memory - small HDD - etc. etc. really make spending any money on replacing the MOB kind of wasteful since you are then going to also need more RAM a faster CPU and a new video card to make any use of that new MOBO meaning your spending quite a bit of $ on what will then still be an obsolete and slower performing system!!
Really think your best option is to save up some $ and just get a new system vs. spending the money to upgrade\fix that 1. To give you some idea here is an E-bay listing for a Dell Dimension 2400 with the 2.4Ghz. Celeron CPU with a buy it now price of $59 (+ $25 Shipping) and they can't even sell it !! ( LINKIE
And another with the P4 2.4 Ghz and 1 GB of RAM that will sell in the next 3 hours with a winning bid right now of $18 (+$22 Shipping) !! ( LINKIE