DHCP and Different Operating Systems

Hello all!

At home I have a Belkin wireless router connected to PlusNet and set to use
DHCP, and I have three clients:

- a Windows XP x64 desktop, which gets an IP address straight away every
time
- a Windows 2000 laptop with a Belkin wireless card, with gets an IP address
95% of the time
- a Dell Axim PDA running Pocket Windows 2003, which never gets an IP
address and I've had to give it a static one.

At work we have an Alcatel Speed Touch router (not wireless) connected to
Nildram and set to use DHCP with 25-30 clients:

- multiple Windows XP PCs - never have a problem with IP addresses
- one Vector Linux laptop - never gets an IP address
- one MacOS 10.x laptop - never gets an IP address

This is more of a problem as we hot-desk and staff use their PCs elsewhere,
so we don't want to fix IP addresses.

My questions are these:

1. the OS appears to be an issue; does anyone know whether it's the DHCP
clients or the servers that are to blame when IP addresses aren't allocated?

2. is there anything I can do to get the PDA, the Linux laptop and the Mac
to pick up dynamically-allocated IP addresses?

Any information would be gratefully received - thanks!

Andrew